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[(a)-474.3(c)3.7(olouring.)-873(T)4.7(herefore,)]TJ /F11 1 Tf 10.9106 0 TD 0 Tc (v)Tj /F9 1 Tf 7.9701 0 0 7.9701 208.08 672.6 Tm (0)Tj /F3 1 Tf 11.9552 0 0 11.9552 218.52 674.4 Tm -0.001 Tc [(will)-482.8(b)-30.1(e)-469.4(xed)-481.8(b)30.1(y)-478.7(ev)33.2(ery)-488.7(a)-3.8(utomorphism)-480.8(of)]TJ /F11 1 Tf 18.1074 0 TD 0 Tc (H)Tj /F3 1 Tf 1.3651 0 TD -0.0013 Tc [(preserving)-496(the)]TJ -31.7283 -1.2045 TD 0.0002 Tc (colouring)Tj /F11 1 Tf 4.1956 0 TD 0 Tc (c)Tj /F3 1 Tf 0.7026 0 TD 0.0004 Tc [(\(later)-282.1(on,)-280.7(w)34.9(e)-287.3(w)4.8(rite)]TJ /F12 1 Tf 8.06 0 TD 0.0018 Tc [(xe)50.3(d)-301.2(by)]TJ /F11 1 Tf 3.4127 0 TD 0 Tc (c)Tj /F3 1 Tf 0.4216 0 TD 0.0007 Tc [(,)-280.4(f)-1.4(or)-281.8(s)5.3(h)1.7(ort\).)-420.9(T)5.1(h)31.8(us)5.3(,)-300.4(w)35.2(e)-287(c)4.1(ons)5.3(i)0.7(der)-291.8(a)-2.1(n)-279.4(i)0.7(nitial)-280.4(s)5.3(ubgraph)]TJ /F11 1 Tf -16.7925 -1.2145 TD 0 Tc (F)Tj /F9 1 Tf 7.9701 0 0 7.9701 79.56 643.6801 Tm (0)Tj /F3 1 Tf 11.9552 0 0 11.9552 87.6 645.48 Tm -0.0017 Tc [(induced)-291.8(b)29.4(y)-278.7(a)-4.5(l)-1.7(l)-272.7(v)32.5(ertices)-298.2(o)-4.5(f)-264.8(dista)-4.5(n)-0.7(ce)-289.4(a)-4.5(t)-274.1(mo)-4.5(st)-284.2(2)-275.5(f)-3.8(ro)-4.5(m)]TJ /F11 1 Tf 21.0282 0 TD 0 Tc (v)Tj /F9 1 Tf 7.9701 0 0 7.9701 344.64 643.6801 Tm (0)Tj /F3 1 Tf 11.9552 0 0 11.9552 349.32 645.48 Tm 0.001 Tc [(.)-420.6(W)83.6(e)-276.7(c)4.4(olour)-271.4(t)-0.4(he)-276.7(e)4.4(d)2(ge)4.4(s)-275.5(o)-1.8(f)]TJ /F11 1 Tf 10.469 0 TD 0 Tc (F)Tj /F9 1 Tf 7.9701 0 0 7.9701 482.04 643.6801 Tm (0)Tj /F3 1 Tf 11.9552 0 0 11.9552 490.08 645.48 Tm -0.0014 Tc [(in)-271.4(suc)32.1(h)]TJ -34.9707 -1.2045 TD 0.0005 Tc [(a)-323.5(w)35(a)27.8(y)-336.7(that)-322.1(eac)34(h)-329.8(v)34.7(e)3.9(rtex)-336.7(o)-2.3(f)]TJ /F11 1 Tf 11.1916 0 TD 0 Tc (F)Tj /F9 1 Tf 7.9701 0 0 7.9701 213.36 629.28 Tm (0)Tj /F3 1 Tf 11.9552 0 0 11.9552 222 631.08 Tm -0.002 Tc [(will)-333.2(b)-31.1(e)-319.8(xed)-332.3(b)29.1(y)]TJ /F11 1 Tf 6.8957 0 TD 0 Tc (c)Tj /F3 1 Tf 0.4216 0 TD -0.0021 Tc [(.)-433.7(T)2.3(hen,)-343.4(w)32.4(e)-329.9(consider)-344.8(a)-326.1(s)2.5(equence)-350(o)-4.9(f)-315.4(i)-2.1(nduced)]TJ -19.8641 -1.2145 TD -0.0003 Tc (subgraphs)Tj /F11 1 Tf 4.7577 0 TD 0 Tc (F)Tj /F9 1 Tf 7.9701 0 0 7.9701 136.44 614.76 Tm (1)Tj /F11 1 Tf 11.9552 0 0 11.9552 141.12 616.5601 Tm 0.1706 Tc (,F)Tj /F9 1 Tf 7.9701 0 0 7.9701 153.96 614.76 Tm 0 Tc (2)Tj /F11 1 Tf 11.9552 0 0 11.9552 158.76 616.5601 Tm 0.1706 Tc (,...)Tj /F3 1 Tf 2.0376 0 TD 0.0028 Tc (of)Tj /F11 1 Tf 1.2346 0 TD 0 Tc (H)Tj /F3 1 Tf 1.335 0 TD -0.0028 Tc [(suc)30.7(h)-463.5(t)-4.2(h)-1.8(a)-5.6(t)]TJ /F11 1 Tf 4.577 0 TD 0 Tc (F)Tj /F10 1 Tf 7.9701 0 0 7.9701 276.12 614.76 Tm (i)Tj /F15 1 Tf 0.3614 0 TD ()Tj /F9 1 Tf 0.8281 0 TD (1)Tj /F3 1 Tf 11.9552 0 0 11.9552 295.68 616.5601 Tm 0.001 Tc [(is)-446.1(a)-453.5(p)2(rop)-28.1(e)4.4(r)-452.1(s)5.6(ubgraph)-449.7(of)]TJ /F11 1 Tf 10.9006 0 TD 0 Tc (F)Tj /F10 1 Tf 7.9701 0 0 7.9701 433.56 614.76 Tm (i)Tj /F3 1 Tf 11.9552 0 0 11.9552 442.32 616.5601 Tm 0.0025 Tc (for)Tj /F11 1 Tf 1.6261 0 TD 0 Tc (i)Tj /F3 1 Tf 0.813 0 TD 0.4836 Tc (=1)Tj /F11 1 Tf 1.7365 0 TD 0 Tc (,)Tj /F3 1 Tf 0.4416 0 TD (2)Tj /F11 1 Tf 0.4918 0 TD 0.1706 Tc (,...)Tj /F3 1 Tf 1.5859 0 TD 0 Tc (.)Tj -37.6707 -1.2045 TD -0.0007 Tc [(Namely)83.7(,)]TJ /F11 1 Tf 3.8443 0 TD 0 Tc (F)Tj /F10 1 Tf 7.9701 0 0 7.9701 125.52 600.36 Tm (i)Tj /F3 1 Tf 11.9552 0 0 11.9552 133.32 602.16 Tm -0.0006 Tc [(is)-377.4(a)-374.8(s)4(ubgraph)-381(induced)-391.1(b)30.5(y)-377.9(the)-378.6(v)33.6(ertices)-387.5(of)]TJ /F11 1 Tf 17.7761 0 TD 0 Tc (F)Tj /F10 1 Tf 7.9701 0 0 7.9701 353.4 600.36 Tm (i)Tj /F15 1 Tf 0.3614 0 TD ()Tj /F9 1 Tf 0.8281 0 TD (1)Tj /F3 1 Tf 11.9552 0 0 11.9552 367.68 602.16 Tm -0.0005 Tc [(,)-381.9(t)-1.9(heir)-383.3(neigh)30.6(b)-29.6(ours)-377.3(and)-380.9(v)33.7(ertices)]TJ -24.7324 -1.2045 TD 0.0008 Tc [(of)-292.4(arms)-285.7(inc)4.2(i)0.8(de)4.2(n)31.9(t)-311.8(to)-283.1(v)35(e)4.2(rtic)4.2(e)4.2(s)-315.8(of)-282.4(de)4.2(gre)4.2(e)-296.9(4)-293.1(o)-2(f)]TJ /F11 1 Tf 17.746 0 TD 0 Tc (F)Tj /F10 1 Tf 7.9701 0 0 7.9701 291.72 585.96 Tm (i)Tj /F15 1 Tf 0.3614 0 TD ()Tj /F9 1 Tf 0.8281 0 TD (1)Tj /F3 1 Tf 11.9552 0 0 11.9552 306 587.76 Tm -0.001 Tc [(.)-422.6(I)0.7(t)-293.5(i)-1(s)-297.5(e)2.4(asily)-298(seen)-301.1(that)-293.5(if)-294.2(w)33.5(e)-298.7(ha)26.3(v)33.2(e)-308.8(dened)-301.1(a)-3.8(n)]TJ -19.5731 -1.2145 TD 0.0002 Tc [(edge)-267.4(colouring)-263.6(o)-2.6(f)]TJ /F11 1 Tf 7.3875 0 TD 0 Tc (F)Tj /F10 1 Tf 7.9701 0 0 7.9701 167.88 571.44 Tm (i)Tj /F15 1 Tf 0.3614 0 TD ()Tj /F9 1 Tf 0.8281 0 TD (1)Tj /F3 1 Tf 11.9552 0 0 11.9552 185.16 573.24 Tm -0.0001 Tc [(x)4(ing)-273.9(e)3.3(ac)33.4(h)-270.1(v)34.1(ertex)-267(o)-2.9(f)]TJ /F11 1 Tf 8.7124 0 TD 0 Tc (F)Tj /F10 1 Tf 7.9701 0 0 7.9701 296.88 571.44 Tm (i)Tj /F15 1 Tf 0.3614 0 TD ()Tj /F9 1 Tf 0.8281 0 TD (1)Tj /F3 1 Tf 11.9552 0 0 11.9552 311.04 573.24 Tm 0.2811 Tc [(,t)279.7(h)282.1(e)284.5(n)]TJ /F11 1 Tf 2.7101 0 TD 0 Tc (F)Tj /F10 1 Tf 7.9701 0 0 7.9701 351 571.44 Tm (i)Tj /F3 1 Tf 11.9552 0 0 11.9552 357.48 573.24 Tm -0.0029 Tc [(m)29.2(u)-1.9(st)-275.3(b)-32(e)-260.5(xed)-283(set)25.8(w)1.5(ise.)-434.5(W)79.7(e)-260.5(extend)]TJ -23.8792 -1.2045 TD 0.0007 Tc [(the)-297(c)4.1(olouring)-313.3(to)-293.2(a)-303.3(s)5.3(uitable)-307.1(c)4.1(olouring)-303.3(of)]TJ /F11 1 Tf 16.7724 0 TD 0 Tc (F)Tj /F10 1 Tf 7.9701 0 0 7.9701 280.08 557.04 Tm (i)Tj /F3 1 Tf 11.9552 0 0 11.9552 287.04 558.84 Tm -0.0002 Tc [(lea)27.1(v)3.9(ing)-314.2(t)-1.6(he)-297.9(colours)-306.8(o)-3(f)-293.4(e)3.2(dges)-306.8(of)]TJ /F11 1 Tf 13.0184 0 TD 0 Tc (F)Tj /F10 1 Tf 7.9701 0 0 7.9701 450.24 557.04 Tm (i)Tj /F15 1 Tf 0.3614 0 TD ()Tj /F9 1 Tf 0.8281 0 TD (1)Tj /F3 1 Tf 11.9552 0 0 11.9552 468 558.84 Tm -0.0004 Tc [(unc)33.1(hanged,)]TJ -33.1238 -1.2045 TD -0.0001 Tc [(and)-330.4(s)4.5(uc)33.4(h)-340.4(t)-1.5(hat)-322.7(t)-1.5(he)-327.9(subgraph)]TJ /F11 1 Tf 12.1653 0 TD 0 Tc (F)Tj /F10 1 Tf 7.9701 0 0 7.9701 225 542.64 Tm (i)Tj /F3 1 Tf 11.9552 0 0 11.9552 232.32 544.44 Tm -0.0019 Tc [(is)-328.6(xed)-342.2(p)-31(o)-4.7(in)29.2(t)26.8(w)2.5(ise.)]TJ /F1 1 Tf -11.9446 -2.1581 TD -0.0009 Tc [(Case)-531.8(1.)]TJ /F3 1 Tf 4.5269 0 TD 0.0003 Tc [(Let)-452.8(u)1.3(s)-456.8()1.3(rs)4.9(t)-462.8(a)-2.5(s)4.9(s)4.9(u)1.3(me)-458(that)]TJ /F11 1 Tf 11.1615 0 TD 0 Tc (H)Tj /F3 1 Tf 1.345 0 TD -0.0016 Tc [(co)-4.4(n)29.5(t)-3(a)-4.4(i)-1.6(ns)-458.7(a)-456.1(v)32.6(ertex)]TJ /F11 1 Tf 7.9897 0 TD 0 Tc (v)Tj /F9 1 Tf 7.9701 0 0 7.9701 394.32 516.84 Tm (0)Tj /F3 1 Tf 11.9552 0 0 11.9552 404.52 518.64 Tm 0.0015 Tc [(of)-452.3(de)4.9(gre)4.9(e)-456.8(4)-453(t)0.1(hat)-441.6(i)1.5(s)-455.6(n)2.5(ot)]TJ -27.8139 -1.2145 TD 0.0006 Tc [(four-armed.)-431(W)83.2(e)-297.1(c)4(olour)-312(i)0.6(ts)-306(three)-307.2(a)-2.2(rms)-306(w)5(ith)-309.6(d)1.6(is)]TJ 19.5929 0 TD -0.0017 Tc [(tinct)-314.3(s)2.9(equences)-338.4(o)-4.5(f)-606.1(co)-4.5(lo)-4.5(urs,)-322.9(a)-4.5(n)-0.7(d)-301.8(i)-1.7(ts)-308.3(inciden)29.4(t)]TJ -19.5929 -1.2045 TD -0.0002 Tc [(p)-29.3(e)3.2(ndan)30.9(t)-342.9(edge)-338.1(w)34.3(e)-348.1(colour)-332.9(with)-340.5(blue.)-472(I)1.5(n)-330.5(o)-3(ur)-342.9(colouring)]TJ /F11 1 Tf 22.4435 0 TD 0 Tc (c)Tj /F3 1 Tf 0.7528 0 TD 0.0012 Tc [(of)-332.2(e)4.6(d)2.2(ge)4.6(s)-345.5(o)-1.6(f)-332.2(t)-0.2(he)-326.6(w)5.6(h)2.2(ole)-346.7(g)-1.6(raph)]TJ /F11 1 Tf 12.1352 0 TD 0 Tc (H)Tj /F3 1 Tf 0.8933 0 TD 0.3312 Tc [(,w)365.7(e)]TJ -36.2248 -1.2045 TD 0.0006 Tc [(ens)5.2(u)1.6(re)-367.4(that)]TJ /F11 1 Tf 5.2295 0 TD 0 Tc (v)Tj /F9 1 Tf 7.9701 0 0 7.9701 140.16 473.52 Tm (0)Tj /F3 1 Tf 11.9552 0 0 11.9552 149.28 475.32 Tm -0.0012 Tc [(is)-358(a)-355.3(unique)-369.2(v)33(ertex)-378.5(o)-4(f)-705.9(d)-0.2(egree)-369.2(4)-355.3(with)-371.6(a)-355.3(b)-0.2(lue)-359.2(i)-1.2(nciden)29.9(t)-384(p)-30.3(endan)29.9(t)-364(edge.)-533.2(T)3.2(h)29.9(u)-0.2(s,)]TJ /F11 1 Tf -6.4642 -1.2145 TD 0 Tc (v)Tj /F9 1 Tf 7.9701 0 0 7.9701 77.64 459 Tm (0)Tj /F3 1 Tf 11.9552 0 0 11.9552 86.28 460.8 Tm -0.002 Tc [(will)-333.2(b)-31.1(e)-319.8(xed)-332.3(b)29.1(y)]TJ /F11 1 Tf 6.8957 0 TD 0 Tc (c)Tj /F3 1 Tf 0.4216 0 TD [(.)-431.6(C)4.4(ons)4.6(e)3.4(q)4.1(u)1(en)31.1(tly)84.4(,)-351.3(all)-331.2(t)-1.4(he)-317.8(v)34.2(e)3.4(rtices)-346.7(of)-313.3(the)-327.8(s)4.6(ubgraph)]TJ /F11 1 Tf 20.5766 0 TD (F)Tj /F9 1 Tf 7.9701 0 0 7.9701 427.32 459 Tm (0)Tj /F3 1 Tf 11.9552 0 0 11.9552 435.96 460.8 Tm -0.0019 Tc [(induced)-332.2(b)29.2(y)]TJ /F11 1 Tf 4.9986 0 TD 0 Tc (v)Tj /F9 1 Tf 7.9701 0 0 7.9701 501.36 459 Tm (0)Tj /F3 1 Tf 11.9552 0 0 11.9552 506.04 460.8 Tm 0.3212 Tc [(,i)321.2(t)319.8(s)]TJ -36.3056 -1.2045 TD 0.0009 Tc [(ne)4.3(igh)32(b)-28.2(ours)-345.8(and)-339.4(e)4.3(nd-v)35.1(e)4.3(rtic)4.3(e)4.3(s)-365.9(of)-332.5(its)-345.8(a)-1.9(rms)5.5(,)-350.4(are)-337(a)-1.9(ls)5.5(o)-343.2()1.9(x)5(e)4.3(d)-349.4(b)32(y)]TJ /F11 1 Tf 24.8725 0 TD 0 Tc (c)Tj /F3 1 Tf 0.4216 0 TD 0.0006 Tc [(.)-481.2(W)83.2(e)-337.3(c)4(olour)-342.1(t)-0.8(he)-347.3(e)4(d)1.6(ge)4(s)-346.1(j)-1.5(oining)]TJ 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TD 0.0002 Tc (colouring)Tj /F11 1 Tf 4.3161 0 TD 0 Tc (c)Tj /F3 1 Tf 0.8231 0 TD 0.0012 Tc [(of)-402.4(the)-406.9(w)5.6(hole)-406.9(graph)]TJ /F11 1 Tf 8.6622 0 TD 0 Tc (H)Tj /F3 1 Tf 1.2948 0 TD 0.0002 Tc [(\(w)4.6(here)]TJ /F11 1 Tf 3.2822 0 TD 0 Tc (v)Tj /F9 1 Tf 7.9701 0 0 7.9701 297.36 698.4 Tm (0)Tj /F3 1 Tf 11.9552 0 0 11.9552 306.96 700.2001 Tm -0.0003 Tc [(is)-397.2(the)-408.4(o)-3.1(nly)-407.7(v)33.9(ertex)-417.8(o)-3.1(f)-393.9(d)0.7(egree)-418.5(4)-394.6(w)4.1(i)-0.3(th)-410.9(a)-404.6(b)0.7(lue)]TJ -19.6534 -1.2145 TD -0.0002 Tc [(p)-29.3(e)3.2(ndan)30.9(t)-332.9(edge\).)]TJ /F1 1 Tf 1.4655 -2.148 TD -0.0009 Tc [(Case)-441.5(2.)]TJ /F3 1 Tf 4.2057 0 TD [(Assume)-399(no)26.4(w)-377.9(t)-2.3(hat)-373.7(a)-3.7(ll)-372.3(v)33.3(e)2.5(rtices)-397.8(of)-374.4(degree)-378.9(4)-375.1(i)-0.9(n)]TJ /F11 1 Tf 19.2516 0 TD 0 Tc (H)Tj /F3 1 Tf 1.2647 0 TD 0.0009 Tc [(are)-367.1(f)-1.2(our-arme)4.3(d.)-581.3(W)83.5(e)-377.1(c)34.4(h)1.9(o)-32(o)-1.9(s)5.5(e)]TJ -26.1875 -1.2145 TD -0.0001 Tc [(an)31(y)-367.4(s)4.5(uc)33.4(h)-380.5(v)34.1(ertex)]TJ /F11 1 Tf 7.1466 0 TD 0 Tc (v)Tj /F9 1 Tf 7.9701 0 0 7.9701 163.08 643.6801 Tm (0)Tj /F3 1 Tf 11.9552 0 0 11.9552 172.2 645.48 Tm 0.0003 Tc [(of)-363.2(de)3.7(gre)3.7(e)-377.7(4)-363.9(a)-2.5(nd)-370.1(fully)-367(c)3.7(o)-2.5(lour)-362.5(its)-376.5(a)-2.5(rms)4.9(.)-561.8(In)-360.1(our)-372.5(c)3.7(olouring)]TJ /F11 1 Tf 23.929 0 TD 0 Tc (c)Tj /F3 1 Tf 0.7829 0 TD 0.0017 Tc [(of)-361.8(all)-369.7(e)5.1(dge)5.1(s)]TJ -33.0933 -1.2045 TD 0.0028 Tc (of)Tj /F11 1 Tf 1.074 0 TD 0 Tc (H)Tj /F3 1 Tf 0.8933 0 TD -0.0006 Tc [(,)-291.7(w)33.9(e)-288.3(e)2.8(nsure)-298.3(t)-2(hat)]TJ /F11 1 Tf 7.0563 0 TD 0 Tc (v)Tj /F9 1 Tf 7.9701 0 0 7.9701 185.52 629.28 Tm (0)Tj /F3 1 Tf 11.9552 0 0 11.9552 193.68 631.08 Tm -0.0002 Tc [(is)-286.7(the)-277.9(o)-3(nly)-287.2(f)-2.3(ully)-287.2(coloured)-300.3(v)34(e)3.2(rtex)-297.2(o)-3(f)-283.4(d)0.8(egree)-287.9(4)-3(.)-421.8(T)4.2(his)-296.7(g)-3(uaran)30.9(t)-1.6(ees)-286.7(that)]TJ /F11 1 Tf -10.178 -1.2145 TD 0 Tc (v)Tj /F9 1 Tf 7.9701 0 0 7.9701 77.64 614.76 Tm (0)Tj /F3 1 Tf 11.9552 0 0 11.9552 87.12 616.5601 Tm 0.0002 Tc [(w)4.6(ill)-401.3(b)-28.9(e)-397.9(x)4.3(e)3.6(d)-410.4(b)31.3(y)-397.2(the)-397.9(c)3.6(olouring)]TJ /F11 1 Tf 13.2593 0 TD 0 Tc (c)Tj /F3 1 Tf 0.4216 0 TD -0.0007 Tc [(.)-643.1(N)0.6(ote)-398.8(t)-2.1(hat)-393.6(t)-2.1(hen)-411.3(a)-3.5(lso)-395(t)-2.1(he)-398.8(v)33.5(e)2.7(rtices)-417.7(lying)-405(o)-3.5(n)-401.2(t)-2.1(he)-398.8(arms)]TJ -14.9456 -1.2045 TD 0.0028 Tc (of)Tj /F11 1 Tf 1.5759 0 TD 0 Tc (v)Tj /F9 1 Tf 7.9701 0 0 7.9701 96.48 600.36 Tm (0)Tj /F3 1 Tf 11.9552 0 0 11.9552 105.96 602.16 Tm -0.002 Tc [(will)-413.5(b)-31.1(e)-390.1(xed)-412.6(b)29.1(y)]TJ /F11 1 Tf 7.1868 0 TD 0 Tc (c)Tj /F3 1 Tf 0.4216 0 TD -0.0002 Tc [(.)-642.6(N)1.1(o)27.1(w)-407.4(w)34.3(e)-398.3(ha)27.1(v)34(e)-408.3(to)-394.5(colour)-403.1(the)-388.3(r)-1.6(emaining)-414.6(edges)-397.1(o)-3(f)-393.8(t)-1.6(he)-398.3(graph)]TJ /F11 1 Tf 26.1875 0 TD 0 Tc (F)Tj /F9 1 Tf 7.9701 0 0 7.9701 517.56 600.36 Tm (0)Tj /F3 1 Tf 11.9552 0 0 11.9552 522.36 602.16 Tm (,)Tj -37.6707 -1.2045 TD -0.0019 Tc [(induced)-352.2(b)29.2(y)]TJ /F11 1 Tf 5.0287 0 TD 0 Tc (v)Tj /F9 1 Tf 7.9701 0 0 7.9701 137.76 585.96 Tm (0)Tj /F3 1 Tf 11.9552 0 0 11.9552 146.52 587.76 Tm -0.0002 Tc [(and)-330.5(t)-1.6(he)-338.1(v)34(e)3.2(rtices)-357(on)-330.5(its)-336.9(a)-3(rms)4.4(.)-472(All)-341.5(v)34(ertices)-357(of)-333.6(the)-338.1(g)-3(raph)]TJ /F11 1 Tf 23.4774 0 TD 0 Tc (F)Tj /F9 1 Tf 7.9701 0 0 7.9701 434.76 585.96 Tm (0)Tj /F3 1 Tf 11.9552 0 0 11.9552 443.52 587.76 Tm 0.0004 Tc [(are)-337.5()1.4(x)4.5(e)3.8(d,)-350.9(s)5(o)-343.7(the)]TJ -31.0761 -1.2145 TD -0.0016 Tc [(co)-4.4(lo)-4.4(ur)-304.1(o)-4.4(f)-304.8(these)-309.4(e)1.8(dg)-4.4(es)-318.2(do)-34.5(es)-298.1(no)-4.4(t)-304.1(m)0.4(a)-4.4(tter)-314.2(f)-3.7(o)-4.4(r)-294.1(a)-4.4(s)]TJ 18.5089 0 TD -0.0006 Tc [(ymmetry)83.8(,)-331.8(but)-303.1(it)-303.1(ma)26.7(y)-307.7(h)0.4(app)-29.7(e)2.8(n)-310.8(t)-2(hat)-303.1(s)4(ome)-308.4(e)2.8(dges)]TJ -18.5089 -1.2045 TD -0.0002 Tc [(are)-348.1(i)-0.2(nciden)30.9(t)-363(w)4.2(ith)-350.5(a)-3(nother)-352.9(v)34(e)3.2(rtex)-357.5(o)-3(f)-343.6(d)0.8(egree)-358.2(4)-3(,)-351.5(a)-3(nd)-340.5(w)34.3(e)-358.2(m)31.9(u)0.8(s)4.4(t)-363(ens)4.4(u)0.8(re)-358.2(that)-342.9(this)-357(v)34(e)3.2(rtex)-357.5(i)-0.2(s)-346.9(n)0.8(ot)]TJ T* -0.0015 Tc [(f)-3.6(u)-0.5(lly)-408.9(co)-4.3(lo)-4.3(ured.)-674(W)81.1(e)-399.6(s)3.1(ha)-4.3(ll)-413(ca)-4.3(ll)-413(ea)-4.3(c)32(h)-412.1(suc)32(h)-412.1(edg)-4.3(e)]TJ /F12 1 Tf 19.7033 0 TD 0.0017 Tc [(a)-421.7(nishing)-411.5(e)50.2(dge)]TJ /F3 1 Tf 6.7551 0 TD -0.0003 Tc [(.)-652.7(F)-3.7(igure)-398.9(1)-404.6(sho)27(w)4.1(s)-417.3(a)-3.1(ll)-401.8(three)]TJ -26.4585 -1.2145 TD 0 Tc [(p)-29.1(o)-2.8(ssible)-378(s)4.6(uc)33.5(h)-380.4(s)4.6(ituations)-376.8(w)4.4(ith)-370.4(s)4.6(uitable)-378(c)3.4(olourings.)-562.1(If)-373.5(four)-362.8(arms)-376.8(of)]TJ /F11 1 Tf 28.2852 0 TD (v)Tj /F9 1 Tf 7.9701 0 0 7.9701 415.8 528.12 Tm (0)Tj /F3 1 Tf 11.9552 0 0 11.9552 424.92 529.92 Tm 0.0012 Tc [(me)4.6(e)4.6(t)-381.6(at)-361.6(one)-366.8(v)35.4(e)4.6(rte)4.6(x)5.3(,)]TJ -29.5203 -1.2045 TD -0.0016 Tc (then)Tj /F11 1 Tf 2.2584 0 TD 0 Tc (F)Tj /F9 1 Tf 7.9701 0 0 7.9701 106.56 513.72 Tm (0)Tj /F3 1 Tf 11.9552 0 0 11.9552 115.32 515.52 Tm (=)Tj /F11 1 Tf 1.0941 0 TD (H)Tj /F3 1 Tf 1.2246 0 TD (=)Tj /F11 1 Tf 1.0941 0 TD (K)Tj /F9 1 Tf 7.9701 0 0 7.9701 166.08 513.72 Tm (4)Tj /F10 1 Tf 0.527 0 TD (,)Tj /F9 1 Tf 0.3011 0 TD (2)Tj /F3 1 Tf 11.9552 0 0 11.9552 177.36 515.52 Tm -0.0009 Tc [(,)-372.3(a)-3.7(n)-351.2(e)2.5(xcluded)-381.3(g)-3.7(raph)-361.3(with)]TJ /F11 1 Tf 11.1816 0 TD 0 Tc (D)Tj /F15 1 Tf 7.9701 0 0 7.9701 321.12 519.84 Tm ()Tj /F3 1 Tf 11.9552 0 0 11.9552 323.88 515.52 Tm (\()Tj /F11 1 Tf 0.3814 0 TD (K)Tj /F9 1 Tf 7.9701 0 0 7.9701 338.4 513.72 Tm (4)Tj /F10 1 Tf 0.527 0 TD (,)Tj /F9 1 Tf 0.3011 0 TD (2)Tj /F3 1 Tf 11.9552 0 0 11.9552 349.68 515.52 Tm 0.0007 Tc [(\))-332(=)-332.4(3.)-531.3(In)-359.7(all)-360.7(o)-2.1(the)4.1(r)-362.1(c)4.1(a)-2.1(s)5.3(e)4.1(s)5.3(,)]TJ /F11 1 Tf 11.1114 0 TD 0 Tc (v)Tj /F9 1 Tf 7.9701 0 0 7.9701 488.16 513.72 Tm (0)Tj /F3 1 Tf 11.9552 0 0 11.9552 497.16 515.52 Tm 0.0001 Tc [(is)-366.7(the)]TJ -35.5629 -1.2145 TD -0.0002 Tc [(only)-367.5(fully)-367.5(coloured)-360.6(v)34(e)3.2(rtex)-377.5(o)-3(f)-363.7(d)0.8(egree)-368.2(4)-364.4(in)]TJ /F11 1 Tf 17.6758 0 TD 0 Tc (F)Tj /F9 1 Tf 7.9701 0 0 7.9701 290.88 499.2 Tm (0)Tj /F3 1 Tf 11.9552 0 0 11.9552 295.56 501 Tm -0.0026 Tc [(.)-544.6(H)-1.3(ence,)-394.1(since)]TJ /F11 1 Tf 6.4841 0 TD 0 Tc (v)Tj /F9 1 Tf 7.9701 0 0 7.9701 378.72 499.2 Tm (0)Tj /F3 1 Tf 11.9552 0 0 11.9552 387.72 501 Tm -0.002 Tc [(is)-368.8(xed)-372.4(b)29.1(y)]TJ /F11 1 Tf 4.828 0 TD 0 Tc (c)Tj /F3 1 Tf 0.4216 0 TD -0.0004 Tc [(,)-371.8(t)-1.8(he)-358.4(subgraph)]TJ /F11 1 Tf -31.6582 -1.2045 TD 0 Tc (F)Tj /F9 1 Tf 7.9701 0 0 7.9701 79.56 484.8 Tm (0)Tj /F3 1 Tf 11.9552 0 0 11.9552 88.2 486.6 Tm -0.0019 Tc [(is)-328.6(also)-336(xed)-342.2(p)-31(o)-4.7(in)29.2(t)26.8(w)2.5(ise.)]TJ ET 0 G 0 J 0 j 0.797 w 10 M []0 d 1 i 158.092 408.96 m 158.092 408.96 l 158.092 411.307 156.187 413.212 153.84 413.212 c 151.493 413.212 149.588 411.307 149.588 408.96 c 149.588 406.613 151.493 404.708 153.84 404.708 c 156.187 404.708 158.092 406.613 158.092 408.96 c h 115.572 437.306 m 115.572 437.306 l 115.572 439.653 113.667 441.558 111.32 441.558 c 108.973 441.558 107.069 439.653 107.069 437.306 c 107.069 434.959 108.973 433.055 111.32 433.055 c 113.667 433.055 115.572 434.959 115.572 437.306 c h 158.092 465.653 m 158.092 465.653 l 158.092 468 156.187 469.905 153.84 469.905 c 151.493 469.905 149.588 468 149.588 465.653 c 149.588 463.306 151.493 461.401 153.84 461.401 c 156.187 461.401 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11.9552 148.2 397.56 Tm 0 Tc (v)Tj /F9 1 Tf 7.9701 0 0 7.9701 153.84 395.76 Tm (0)Tj ET 0 1 0 RG 2.835 w 114.858 434.948 m 150.302 411.318 l 114.858 439.665 m 150.302 463.294 l 141.568 433.504 m 151.939 412.763 l S 0 0 1 RG 141.568 441.109 m 151.939 461.85 l 166.112 433.504 m 155.741 412.763 l S 0 1 0 RG 166.112 441.109 m 155.741 461.85 l S 0 0 1 RG 192.822 434.948 m 157.378 411.318 l 196.36 441.558 m 196.36 461.401 l S 0 1 0 RG 158.092 465.653 m 192.108 465.653 l S 0 G 0.797 w 299.812 408.96 m 299.812 408.96 l 299.812 411.307 297.907 413.212 295.56 413.212 c 293.213 413.212 291.308 411.307 291.308 408.96 c 291.308 406.613 293.213 404.708 295.56 404.708 c 297.907 404.708 299.812 406.613 299.812 408.96 c h 257.292 437.306 m 257.292 437.306 l 257.292 439.653 255.387 441.558 253.04 441.558 c 250.693 441.558 248.789 439.653 248.789 437.306 c 248.789 434.959 250.693 433.055 253.04 433.055 c 255.387 433.055 257.292 434.959 257.292 437.306 c h 299.812 465.653 m 299.812 465.653 l 299.812 468 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Tf 1.887 0 TD 0.0389 Tc (vx)Tj /F9 1 Tf 7.9701 0 0 7.9701 379.92 683.88 Tm 0 Tc (2)Tj /F11 1 Tf 11.9552 0 0 11.9552 384.6 685.6801 Tm (u)Tj /F9 1 Tf 7.9701 0 0 7.9701 391.32 683.88 Tm (2)Tj /F3 1 Tf 11.9552 0 0 11.9552 396 685.6801 Tm -0.0021 Tc [(.)-433.7(L)-3.4(et)-314.7(us)-318.7(co)-4.9(nsider)-324.7(rst)-324.7(the)]TJ -27.1013 -1.2045 TD 0.0004 Tc [(c)3.8(a)-2.4(s)5(e)-287.3(w)4.8(h)1.4(e)3.8(n)-279.7(b)-28.7(o)-2.4(th)-279.7(arms)-276.1(are)-267.2(nis)5(h)1.4(ing.)-441.3(If)]TJ /F11 1 Tf 15.9393 0 TD 0 Tc (u)Tj /F9 1 Tf 7.9701 0 0 7.9701 269.28 669.48 Tm (1)Tj /F2 1 Tf 11.9552 0 0 11.9552 277.32 671.28 Tm ()Tj /F3 1 Tf T* (=)Tj /F11 1 Tf 1.0338 0 TD (u)Tj /F9 1 Tf 7.9701 0 0 7.9701 296.4 669.48 Tm (2)Tj /F3 1 Tf 11.9552 0 0 11.9552 301.08 671.28 Tm 0.001 Tc [(,)-290.1(w)35.5(e)-286.7()2(rs)5.6(t)-281.5(c)4.4(olour)-281.5(t)-0.4(he)-276.7(arm)]TJ /F11 1 Tf 10.4087 0 TD 0.0389 Tc (vx)Tj /F9 1 Tf 7.9701 0 0 7.9701 438.24 669.48 Tm 0 Tc (1)Tj /F11 1 Tf 11.9552 0 0 11.9552 443.04 671.28 Tm (u)Tj /F9 1 Tf 7.9701 0 0 7.9701 449.76 669.48 Tm (1)Tj /F3 1 Tf 11.9552 0 0 11.9552 457.68 671.28 Tm -0.0014 Tc [(in)-281.5(suc)32.1(h)-291.5(a)-285.3(w)33.1(a)25.9(y)]TJ -32.2605 -1.2045 TD 0.0002 Tc [(that)-322.4(the)-327.6(v)34.4(ertex)]TJ /F11 1 Tf 6.7652 0 TD 0 Tc (u)Tj /F9 1 Tf 7.9701 0 0 7.9701 159.6 655.08 Tm (1)Tj /F3 1 Tf 11.9552 0 0 11.9552 168.12 656.88 Tm 0.0007 Tc [(is)-326(not)-332(f)-1.4(ully)-326.4(c)4.1(o)-2.1(loure)4.1(d)1.7(,)-330.5(w)5.1(hic)34.2(h)-339.6(is)-326(again)-319.5(a)-2.1(n)-319.5(e)4.1(as)5.3(y)-326.4(t)-0.7(as)5.3(k)4.8(.)-441(T)5.1(h)31.8(us)5.3(,)-340.6(o)-2.1(nly)-326.4(o)-2.1(ne)-327.1(arm)]TJ /F11 1 Tf -8.04 -1.2145 TD 0.0389 Tc (vx)Tj /F9 1 Tf 7.9701 0 0 7.9701 84.72 640.5601 Tm 0 Tc (2)Tj /F11 1 Tf 11.9552 0 0 11.9552 89.52 642.36 Tm (u)Tj /F9 1 Tf 7.9701 0 0 7.9701 96.24 640.5601 Tm (2)Tj /F3 1 Tf 11.9552 0 0 11.9552 104.28 642.36 Tm -0.001 Tc [(is)-297.5(lef)-3.1(t)-2.4(,)-292.1(a)-3.8(nd)-291.1(w)33.5(e)-298.7(pro)-33.9(ceed)-291.1(with)-301.1(this)-287.5(a)-3.8(r)-2.4(m)-290.1(a)-3.8(s)-287.5(i)-1(n)-291.1(t)-2.4(he)-288.7(previo)-3.8(us)-297.5(pa)-3.8(ra)-3.8(g)-3.8(r)-2.4(a)-3.8(ph.)-422.6(If)]TJ /F11 1 Tf 29.5499 0 TD 0 Tc (u)Tj /F9 1 Tf 7.9701 0 0 7.9701 464.28 640.5601 Tm (1)Tj /F3 1 Tf 11.9552 0 0 11.9552 472.2 642.36 Tm (=)Tj /F11 1 Tf 1.0439 0 TD (u)Tj /F9 1 Tf 7.9701 0 0 7.9701 491.4 640.5601 Tm (2)Tj /F3 1 Tf 11.9552 0 0 11.9552 496.08 642.36 Tm 0.2911 Tc [(,t)289.7(h)292.1(e)294.5(n)]TJ -35.4725 -1.2045 TD 0.0003 Tc [(w)34.8(e)-317.5(colour)-302.2(the)-307.5(a)-2.5(rm)]TJ /F11 1 Tf 7.9998 0 TD 0.0389 Tc (vx)Tj /F9 1 Tf 7.9701 0 0 7.9701 180.36 626.16 Tm 0 Tc (1)Tj /F11 1 Tf 11.9552 0 0 11.9552 185.16 627.96 Tm (u)Tj /F9 1 Tf 7.9701 0 0 7.9701 191.88 626.16 Tm (1)Tj /F3 1 Tf 11.9552 0 0 11.9552 200.16 627.96 Tm 0.0007 Tc [(w)5.1(i)0.7(th)-309.5(a)-313.3(c)4.1(olouring)-313.3(us)5.3(e)4.1(d)-309.5(for)-301.8(a)-2.1(nothe)4.1(r)-311.9(alre)4.1(ady)-306.4(c)4.1(oloure)4.1(d)-319.5(a)-2.1(rm)-298.5(inc)4.1(i)0.7(de)4.1(n)31.8(t)]TJ -10.72 -1.2045 TD 0.0014 Tc (to)Tj /F11 1 Tf 1.1744 0 TD 0 Tc (v)Tj /F3 1 Tf 0.5119 0 TD -0.0029 Tc [(.)-424.5(H)-1.6(ence,)]TJ /F11 1 Tf 3.8543 0 TD 0 Tc (v)Tj /F3 1 Tf 0.813 0 TD -0.0002 Tc [(will)-301.3(not)-302.7(b)-29.3(e)-308(f)-2.3(ully)-297.2(coloured.)-441.9(N)1.1(ext,)-311.4(w)34.3(e)-308(colour)-302.7(the)-308(a)-3(rm)]TJ /F11 1 Tf 21.9617 0 TD 0.0389 Tc (vx)Tj /F9 1 Tf 7.9701 0 0 7.9701 423.24 611.76 Tm 0 Tc (2)Tj /F11 1 Tf 11.9552 0 0 11.9552 427.92 613.5601 Tm (u)Tj /F9 1 Tf 7.9701 0 0 7.9701 434.64 611.76 Tm (1)Tj /F3 1 Tf 11.9552 0 0 11.9552 442.92 613.5601 Tm 0.0007 Tc [(w)5.1(i)0.7(th)-309.5(a)-303.3(c)4.1(olouring)]TJ -31.0259 -1.2145 TD 0.0012 Tc [(of)-302(an)-298.9(alre)4.6(ady)-305.9(c)4.6(oloure)4.6(d)-319(a)-1.6(rm)-297.9(inc)4.6(i)1.2(de)4.6(n)32.3(t)-321.4(to)]TJ /F11 1 Tf 16.6319 0 TD 0 Tc (u)Tj /F3 1 Tf 0.8632 0 TD -0.0005 Tc [(whic)33(h)-320.7(i)-0.5(s)-307.1(d)0.5(ieren)30.6(t)-323.1(f)-2.6(rom)-299.6(t)-1.9(hat)-313.1(o)-3.3(f)]TJ /F11 1 Tf 13.0787 0 TD 0.0389 Tc (vx)Tj /F9 1 Tf 7.9701 0 0 7.9701 450.24 597.24 Tm 0 Tc (1)Tj /F11 1 Tf 11.9552 0 0 11.9552 454.92 599.04 Tm (u)Tj /F9 1 Tf 7.9701 0 0 7.9701 461.64 597.24 Tm (1)Tj /F3 1 Tf 11.9552 0 0 11.9552 466.32 599.04 Tm 0.4316 Tc [(.T)436(h)462.7(u)432.6(s)436.2(,)]TJ /F11 1 Tf 3.4328 0 TD 0 Tc (u)Tj /F3 1 Tf 0.8632 0 TD (is)Tj -37.2792 -1.2045 TD -0.0004 Tc [(also)-334.5(not)-323(f)-2.5(ully)-327.5(coloured.)]TJ 1.4655 -1.2145 TD 0.0004 Tc [(If)-333(at)-322.2(le)3.8(as)5(t)-322.2(o)-2.4(ne)-327.4(the)3.8(s)5(e)-337.5(t)29.1(w)34.9(o)-333.7(arms)5(,)-320.8(s)5(a)27.7(y)]TJ /F11 1 Tf 14.9657 0 TD 0.0389 Tc [(vx)42.8(u)]TJ /F9 1 Tf 7.9701 0 0 7.9701 287.88 568.32 Tm 0 Tc (2)Tj /F3 1 Tf 11.9552 0 0 11.9552 292.56 570.12 Tm -0.0003 Tc [(,)-321.5(i)-0.3(s)-327(n)0.7(ot)-322.9(nishing,)-341.6(then)-330.6(w)34.2(e)-328.1(rst)-333(colour)-322.9(the)-328.1(a)-3.1(rm)]TJ /F11 1 Tf -18.4489 -1.2045 TD 0.0389 Tc [(vx)42.8(u)]TJ /F9 1 Tf 7.9701 0 0 7.9701 91.44 553.92 Tm 0 Tc (1)Tj /F3 1 Tf 11.9552 0 0 11.9552 101.04 555.72 Tm 0.0022 Tc [(as)-394.7(ab)-26.9(o)29.5(v)36.4(e)5.6(,)-439.5(s)6.8(u)3.2(c)35.7(h)-418.4(that)]TJ /F11 1 Tf 8.9232 0 TD 0 Tc (u)Tj /F9 1 Tf 7.9701 0 0 7.9701 214.44 553.92 Tm (1)Tj /F3 1 Tf 11.9552 0 0 11.9552 223.92 555.72 Tm -0.0001 Tc [(is)-407.1(not)-413.1(f)-2.2(ully)-407.5(coloured.)-682.7(N)1.2(ext,)-441.8(w)34.4(e)-408.2(colour)-413.1(the)-408.2(a)-2.9(rm)]TJ /F11 1 Tf 20.9078 0 TD 0.0389 Tc [(vx)42.8(u)]TJ /F9 1 Tf 7.9701 0 0 7.9701 493.32 553.92 Tm 0 Tc (2)Tj /F3 1 Tf 11.9552 0 0 11.9552 502.8 555.72 Tm -0.0022 Tc [(wit)-3.6(h)]TJ -36.0346 -1.2045 TD 0.0008 Tc [(a)-323.2(c)4.2(olouring)-333.3(alre)4.2(ady)-336.4(u)1.8(s)5.4(e)4.2(d)-339.5(f)-1.3(or)-321.8(anothe)4.2(r)-331.9(a)-2(rm)-318.4(inc)4.2(i)0.8(de)4.2(n)31.9(t)-351.9(to)]TJ /F11 1 Tf 22.7848 0 TD 0 Tc (v)Tj /F3 1 Tf 0.5119 0 TD -0.0029 Tc [(.)-444.6(H)-1.6(ence,)]TJ /F11 1 Tf 3.8945 0 TD 0 Tc (v)Tj /F3 1 Tf 0.8331 0 TD -0.0001 Tc [(is)-326.8(not)-332.8(f)-2.2(ully)-327.2(coloured.)-451.8(I)1.6(f)]TJ -28.0243 -1.2145 TD -0.0004 Tc [(none)-328.2(of)-323.7(these)-338.3(t)28.3(w)34.1(o)-334.5(arms)-327.1(is)-327.1(nishing)-344.5(w)34.1(e)-328.2(c)3(olour)-333.1(t)-1.8(hem)-329.7(w)4(ith)-330.7(t)28.3(w)34.1(o)-334.5(distinct)-343.1(colourings,)-331.6(u)0.6(sing)-334.5(at)]TJ 0 -1.2045 TD -0.0007 Tc [(least)-333.4(o)-3.5(ne)-328.5(colouring)-334.8(a)-3.5(lready)-327.8(used.)]TJ 1.4655 -1.2145 TD -0.0011 Tc [(Finally)83.3(,)-382.5(c)2.3(onsider)-373.9(t)-2.5(he)-359.1(case)-369.1(when)]TJ /F11 1 Tf 13.8415 0 TD 0 Tc (v)Tj /F3 1 Tf 0.8632 0 TD -0.0004 Tc [(has)-367.2(t)-1.8(hree)-368.4(arms)-357.2(outside)]TJ /F11 1 Tf 10.1678 0 TD 0 Tc (F)Tj /F10 1 Tf 7.9701 0 0 7.9701 394.44 496.08 Tm (i)Tj /F15 1 Tf 0.3614 0 TD ()Tj /F9 1 Tf 0.8281 0 TD (1)Tj /F3 1 Tf 11.9552 0 0 11.9552 408.72 497.88 Tm 0.3714 Tc [(,s)376(a)398.7(y)]TJ /F11 1 Tf 2.3688 0 TD 0.0389 Tc (vx)Tj /F9 1 Tf 7.9701 0 0 7.9701 449.76 496.08 Tm 0 Tc (1)Tj /F11 1 Tf 11.9552 0 0 11.9552 454.44 497.88 Tm (u)Tj /F9 1 Tf 7.9701 0 0 7.9701 461.16 496.08 Tm (1)Tj /F3 1 Tf 11.9552 0 0 11.9552 465.84 497.88 Tm (,)Tj /F11 1 Tf 0.6424 0 TD 0.0389 Tc (vx)Tj /F9 1 Tf 7.9701 0 0 7.9701 486.24 496.08 Tm 0 Tc (2)Tj /F11 1 Tf 11.9552 0 0 11.9552 491.04 497.88 Tm (u)Tj /F9 1 Tf 7.9701 0 0 7.9701 497.76 496.08 Tm (2)Tj /F3 1 Tf 11.9552 0 0 11.9552 506.76 497.88 Tm 0.0009 Tc (and)Tj /F11 1 Tf -36.3659 -1.2045 TD 0.0389 Tc (vx)Tj /F9 1 Tf 7.9701 0 0 7.9701 84.72 481.68 Tm 0 Tc (3)Tj /F11 1 Tf 11.9552 0 0 11.9552 89.52 483.48 Tm (u)Tj /F9 1 Tf 7.9701 0 0 7.9701 96.24 481.68 Tm (3)Tj /F3 1 Tf 11.9552 0 0 11.9552 100.92 483.48 Tm -0.0003 Tc [(,)-401.8(a)-3.1(nd)-380.7(let)-393.2(u)0.7(s)-397.2(s)4.3(upp)-29.4(ose)-388.4(t)-1.7(hat)-393.2(a)-3.1(ll)-381.7(arms)-387.2(are)-388.4(nishing.)-632.7(If)]TJ /F11 1 Tf 22.4435 0 TD 0 Tc (u)Tj /F9 1 Tf 7.9701 0 0 7.9701 375.96 481.68 Tm (1)Tj /F2 1 Tf 11.9552 0 0 11.9552 385.2 483.48 Tm ()Tj /F3 1 Tf T* (=)Tj /F11 1 Tf 1.1443 0 TD (u)Tj /F9 1 Tf 7.9701 0 0 7.9701 405.6 481.68 Tm (2)Tj /F3 1 Tf 11.9552 0 0 11.9552 414.84 483.48 Tm 0.0009 Tc (and)Tj /F11 1 Tf 1.9673 0 TD 0 Tc (u)Tj /F9 1 Tf 7.9701 0 0 7.9701 445.08 481.68 Tm (1)Tj /F2 1 Tf 11.9552 0 0 11.9552 454.32 483.48 Tm ()Tj /F3 1 Tf T* (=)Tj /F11 1 Tf 1.1443 0 TD (u)Tj /F9 1 Tf 7.9701 0 0 7.9701 474.72 481.68 Tm (3)Tj /F3 1 Tf 11.9552 0 0 11.9552 479.4 483.48 Tm 0.4015 Tc [(,w)436(e)13.4()402.5(r)400.1(s)406.1(t)]TJ -34.0773 -1.2045 TD 0.0003 Tc [(colour)-342.4(the)-337.6(a)-2.5(rm)]TJ /F11 1 Tf 6.6748 0 TD 0.0389 Tc (vx)Tj /F9 1 Tf 7.9701 0 0 7.9701 164.52 467.28 Tm 0 Tc (1)Tj /F11 1 Tf 11.9552 0 0 11.9552 169.32 469.08 Tm (u)Tj /F9 1 Tf 7.9701 0 0 7.9701 176.04 467.28 Tm (1)Tj /F3 1 Tf 11.9552 0 0 11.9552 184.68 469.08 Tm 0.0002 Tc [(in)-350.1(s)4.8(u)1.2(c)33.7(h)-350.1(a)-343.9(w)34.7(a)27.5(y)-347(that)-332.5(the)-347.7(v)34.4(ertex)]TJ /F11 1 Tf 13.0184 0 TD 0 Tc (u)Tj /F9 1 Tf 7.9701 0 0 7.9701 347.04 467.28 Tm (1)Tj /F3 1 Tf 11.9552 0 0 11.9552 355.8 469.08 Tm -0.0001 Tc [(is)-336.8(not)-342.8(f)-2.2(ully)-347.3(coloured,)-351.4(i.e.)-481.9(w)4.3(ith)-340.4(a)-2.9(n)]TJ -23.7387 -1.2145 TD 0.0013 Tc [(alre)4.7(ady)-285.7(u)2.3(s)5.9(e)4.7(d)-298.8(c)4.7(olouring)-292.6(of)-281.9(an)-288.8(arm)-277.8(a)-1.5(t)]TJ /F11 1 Tf 15.3471 0 TD 0 Tc (u)Tj /F9 1 Tf 7.9701 0 0 7.9701 262.2 452.76 Tm (1)Tj /F3 1 Tf 11.9552 0 0 11.9552 266.88 454.56 Tm -0.0022 Tc [(.)-423.8(T)2.2(h)28.9(u)-1.2(s,)-313.4(t)26.5(w)32.3(o)-296.1(a)-5(rms)-288.7(i)-2.2(nciden)28.9(t)-314.8(t)-3.6(o)]TJ /F11 1 Tf 12.4262 0 TD 0 Tc (v)Tj /F3 1 Tf 0.803 0 TD 0.0006 Tc 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TD -0.0006 Tc [(\))-273(=)-283.5(2,)-311.8(unless)]TJ /F11 1 Tf 5.651 0 TD 0 Tc (G)Tj /F3 1 Tf 1.0439 0 TD (=)Tj /F11 1 Tf 1.0439 0 TD (L)Tj /F3 1 Tf 0.6625 0 TD (\()Tj /F11 1 Tf 0.3814 0 TD (K)Tj /F9 1 Tf 7.9701 0 0 7.9701 497.28 698.4 Tm (3)Tj /F10 1 Tf 0.527 0 TD (,)Tj /F9 1 Tf 0.3011 0 TD (3)Tj /F3 1 Tf 11.9552 0 0 11.9552 508.68 700.2001 Tm 0.2724 Tc (\)=)Tj /F11 1 Tf -36.5265 -1.2145 TD 0 Tc (K)Tj /F9 1 Tf 7.9701 0 0 7.9701 81.96 683.88 Tm (3)Tj /F16 1 Tf 11.9552 0 0 11.9552 86.64 685.6801 Tm ()Tj /F11 1 Tf 0.7428 0 TD (K)Tj /F9 1 Tf 7.9701 0 0 7.9701 105.48 683.88 Tm (3)Tj /F3 1 Tf 11.9552 0 0 11.9552 114.24 685.6801 Tm 0.0028 Tc (or)Tj /F11 1 Tf 1.1944 0 TD 0 Tc (G)Tj /F3 1 Tf 1.0539 0 TD (=)Tj /F11 1 Tf 1.0338 0 TD (L)Tj /F3 1 Tf 0.6625 0 TD (\()Tj /F11 1 Tf 0.3814 0 TD (K)Tj /F9 1 Tf 7.9701 0 0 7.9701 175.92 683.88 Tm (4)Tj /F10 1 Tf 0.527 0 TD (,)Tj /F9 1 Tf 0.3011 0 TD (2)Tj /F3 1 Tf 11.9552 0 0 11.9552 187.32 685.6801 Tm 0.2724 Tc (\)=)Tj /F11 1 Tf 1.6963 0 TD 0 Tc (K)Tj /F9 1 Tf 7.9701 0 0 7.9701 217.56 683.88 Tm (4)Tj /F16 1 Tf 11.9552 0 0 11.9552 222.24 685.6801 Tm ()Tj /F11 1 Tf 0.7428 0 TD (K)Tj /F9 1 Tf 7.9701 0 0 7.9701 241.08 683.88 Tm (2)Tj /F3 1 Tf 11.9552 0 0 11.9552 245.88 685.6801 Tm (.)Tj -13.0789 -1.2045 TD 0.0002 Tc [(T)84.9(o)-343.9(complete)-347.7(the)-337.7(p)1.2(ro)-32.7(of,)-331(w)34.7(e)-337.7(h)1.2(a)27.5(v)34.4(e)-347.7(t)-1.2(o)-343.9(s)4.8(ho)27.5(w)-336.7(t)-1.2(hat)]TJ /F11 1 Tf 19.6331 0 TD 0 Tc (D)Tj /F3 1 Tf 0.8431 0 TD (\()Tj /F11 1 Tf 0.3814 0 TD (G)Tj /F3 1 Tf 0.7729 0 TD 0.0016 Tc [(\))-280.9(=)-301.4(2)-332.5(f)-0.5(or)-331.1(e)5(v)35.8(e)5(r)0.2(y)-345.6(c)5(oun)32.7(t)0.2(able)-346.3(c)5(l)1.6(a)28.9(w)6(-fre)5(e)]TJ -23.096 -1.2045 TD (graph)Tj /F11 1 Tf 2.7703 0 TD 0 Tc (G)Tj /F3 1 Tf 1.1041 0 TD -0.0024 Tc [(suc)31.1(h)-342.7(t)-3.8(h)-1.4(a)-5.2(t)-325(\()]TJ /F11 1 Tf 5.5205 0 TD 0 Tc (G)Tj /F3 1 Tf 0.7729 0 TD 0.2827 Tc (\)=4)Tj /F11 1 Tf 2.1982 0 TD 0.1706 Tc (,m)Tj /F3 1 Tf 1.2948 0 TD 0 Tc (\()Tj /F11 1 Tf 0.3814 0 TD (G)Tj /F3 1 Tf 0.7729 0 TD (\))Tj /F8 1 Tf 0.6524 0 TD ()Tj /F3 1 Tf 1.0539 0 TD 0.0019 Tc [(4,)-319.3(and)]TJ /F11 1 Tf 2.9911 0 TD 0 Tc (G)Tj /F3 1 Tf 1.1041 0 TD 0.0006 Tc [(is)-326.1(not)-322(t)-0.8(he)-327.2(line)-327.2(g)-2.2(raph)-329.7(of)-322.7(an)31.7(y)-326.5(g)-2.2(raph.)]TJ ET 0 G 0 J 0 j 0.797 w 10 M []0 d 1 i 129.745 583.2 m 129.745 583.2 l 129.745 585.547 127.841 587.452 125.494 587.452 c 123.147 587.452 121.242 585.547 121.242 583.2 c 121.242 580.853 123.147 578.948 125.494 578.948 c 127.841 578.948 129.745 580.853 129.745 583.2 c h 158.092 569.027 m 158.092 569.027 l 158.092 571.374 156.187 573.279 153.84 573.279 c 151.493 573.279 149.588 571.374 149.588 569.027 c 149.588 566.68 151.493 564.775 153.84 564.775 c 156.187 564.775 158.092 566.68 158.092 569.027 c h 186.438 583.2 m 186.438 583.2 l 186.438 585.547 184.533 587.452 182.186 587.452 c 179.839 587.452 177.935 585.547 177.935 583.2 c 177.935 580.853 179.839 578.948 182.186 578.948 c 184.533 578.948 186.438 580.853 186.438 583.2 c h 158.092 597.373 m 158.092 597.373 l 158.092 599.72 156.187 601.625 153.84 601.625 c 151.493 601.625 149.588 599.72 149.588 597.373 c 149.588 595.026 151.493 593.121 153.84 593.121 c 156.187 593.121 158.092 595.026 158.092 597.373 c h 129.296 581.299 m 150.037 570.928 l 157.643 570.928 m 178.384 581.299 l 178.384 585.101 m 157.643 595.472 l 150.037 595.472 m 129.296 585.101 l 153.84 573.279 m 153.84 593.121 l 158.092 625.72 m 158.092 625.72 l 158.092 628.067 156.187 629.971 153.84 629.971 c 151.493 629.971 149.588 628.067 149.588 625.72 c 149.588 623.373 151.493 621.468 153.84 621.468 c 156.187 621.468 158.092 623.373 158.092 625.72 c h 127.852 586.738 m 151.482 622.182 l 156.198 622.182 m 179.828 586.738 l 228.985 583.2 m 228.985 583.2 l 228.985 585.547 227.081 587.452 224.734 587.452 c 222.387 587.452 220.482 585.547 220.482 583.2 c 220.482 580.853 222.387 578.948 224.734 578.948 c 227.081 578.948 228.985 580.853 228.985 583.2 c h 257.332 569.027 m 257.332 569.027 l 257.332 571.374 255.427 573.279 253.08 573.279 c 250.733 573.279 248.828 571.374 248.828 569.027 c 248.828 566.68 250.733 564.775 253.08 564.775 c 255.427 564.775 257.332 566.68 257.332 569.027 c h 285.678 583.2 m 285.678 583.2 l 285.678 585.547 283.773 587.452 281.426 587.452 c 279.079 587.452 277.175 585.547 277.175 583.2 c 277.175 580.853 279.079 578.948 281.426 578.948 c 283.773 578.948 285.678 580.853 285.678 583.2 c h 257.332 597.373 m 257.332 597.373 l 257.332 599.72 255.427 601.625 253.08 601.625 c 250.733 601.625 248.828 599.72 248.828 597.373 c 248.828 595.026 250.733 593.121 253.08 593.121 c 255.427 593.121 257.332 595.026 257.332 597.373 c h 228.536 581.299 m 249.277 570.928 l 256.883 570.928 m 277.624 581.299 l 277.624 585.101 m 256.883 595.472 l 249.277 595.472 m 228.536 585.101 l 253.08 573.279 m 253.08 593.121 l 228.985 611.546 m 228.985 611.546 l 228.985 613.893 227.081 615.798 224.734 615.798 c 222.387 615.798 220.482 613.893 220.482 611.546 c 220.482 609.199 222.387 607.295 224.734 607.295 c 227.081 607.295 228.985 609.199 228.985 611.546 c h 285.678 611.546 m 285.678 611.546 l 285.678 613.893 283.773 615.798 281.426 615.798 c 279.079 615.798 277.175 613.893 277.175 611.546 c 277.175 609.199 279.079 607.295 281.426 607.295 c 283.773 607.295 285.678 609.199 285.678 611.546 c h 224.734 587.452 m 224.734 607.295 l 281.426 607.295 m 281.426 587.452 l 328.225 583.2 m 328.225 583.2 l 328.225 585.547 326.321 587.452 323.974 587.452 c 321.627 587.452 319.722 585.547 319.722 583.2 c 319.722 580.853 321.627 578.948 323.974 578.948 c 326.321 578.948 328.225 580.853 328.225 583.2 c h 356.572 569.027 m 356.572 569.027 l 356.572 571.374 354.667 573.279 352.32 573.279 c 349.973 573.279 348.068 571.374 348.068 569.027 c 348.068 566.68 349.973 564.775 352.32 564.775 c 354.667 564.775 356.572 566.68 356.572 569.027 c h 384.918 583.2 m 384.918 583.2 l 384.918 585.547 383.013 587.452 380.666 587.452 c 378.319 587.452 376.415 585.547 376.415 583.2 c 376.415 580.853 378.319 578.948 380.666 578.948 c 383.013 578.948 384.918 580.853 384.918 583.2 c h 356.572 597.373 m 356.572 597.373 l 356.572 599.72 354.667 601.625 352.32 601.625 c 349.973 601.625 348.068 599.72 348.068 597.373 c 348.068 595.026 349.973 593.121 352.32 593.121 c 354.667 593.121 356.572 595.026 356.572 597.373 c s 327.776 581.299 m 348.517 570.928 l 356.123 570.928 m 376.864 581.299 l 376.864 585.101 m 356.123 595.472 l 348.517 595.472 m 327.776 585.101 l 352.32 573.279 m 352.32 593.121 l 328.225 625.72 m 328.225 625.72 l 328.225 628.067 326.321 629.971 323.974 629.971 c 321.627 629.971 319.722 628.067 319.722 625.72 c 319.722 623.373 321.627 621.468 323.974 621.468 c 326.321 621.468 328.225 623.373 328.225 625.72 c h 384.918 625.72 m 384.918 625.72 l 384.918 628.067 383.013 629.971 380.666 629.971 c 378.319 629.971 376.415 628.067 376.415 625.72 c 376.415 623.373 378.319 621.468 380.666 621.468 c 383.013 621.468 384.918 623.373 384.918 625.72 c h 323.974 587.452 m 323.974 621.468 l 380.666 621.468 m 380.666 587.452 l 376.415 625.72 m 328.225 625.72 l 427.465 597.36 m 427.465 597.36 l 427.465 599.707 425.561 601.612 423.214 601.612 c 420.867 601.612 418.962 599.707 418.962 597.36 c 418.962 595.013 420.867 593.108 423.214 593.108 c 425.561 593.108 427.465 595.013 427.465 597.36 c h 455.812 583.187 m 455.812 583.187 l 455.812 585.534 453.907 587.439 451.56 587.439 c 449.213 587.439 447.308 585.534 447.308 583.187 c 447.308 580.84 449.213 578.935 451.56 578.935 c 453.907 578.935 455.812 580.84 455.812 583.187 c h 484.158 597.36 m 484.158 597.36 l 484.158 599.707 482.253 601.612 479.906 601.612 c 477.559 601.612 475.655 599.707 475.655 597.36 c 475.655 595.013 477.559 593.108 479.906 593.108 c 482.253 593.108 484.158 595.013 484.158 597.36 c h 455.812 611.533 m 455.812 611.533 l 455.812 613.88 453.907 615.785 451.56 615.785 c 449.213 615.785 447.308 613.88 447.308 611.533 c 447.308 609.186 449.213 607.281 451.56 607.281 c 453.907 607.281 455.812 609.186 455.812 611.533 c h 427.016 595.459 m 447.757 585.088 l 455.363 585.088 m 476.104 595.459 l 476.104 599.261 m 455.363 609.632 l 447.757 609.632 m 427.016 599.261 l 451.56 587.439 m 451.56 607.281 l 427.465 625.706 m 427.465 625.706 l 427.465 628.053 425.561 629.958 423.214 629.958 c 420.867 629.958 418.962 628.053 418.962 625.706 c 418.962 623.359 420.867 621.455 423.214 621.455 c 425.561 621.455 427.465 623.359 427.465 625.706 c h 484.158 569.014 m 484.158 569.014 l 484.158 571.361 482.253 573.265 479.906 573.265 c 477.559 573.265 475.655 571.361 475.655 569.014 c 475.655 566.667 477.559 564.762 479.906 564.762 c 482.253 564.762 484.158 566.667 484.158 569.014 c h 423.214 601.612 m 423.214 621.455 l 447.757 613.435 m 427.016 623.805 l 479.906 573.265 m 479.906 593.108 l 476.104 570.915 m 455.363 581.285 l S BT 11.9552 0 0 11.9552 192.96 530.4 Tm 0.0008 Tc [(Figure)-327(2:)-430.9(Be)4.2(ine)4.2(k)35(e)-347.1(g)-2(raphs)]TJ /F11 1 Tf 11.0813 0 TD 0 Tc (B)Tj /F9 1 Tf 7.9701 0 0 7.9701 334.32 528.6 Tm (1)Tj /F3 1 Tf 11.9552 0 0 11.9552 339 530.4 Tm (,)Tj /F11 1 Tf 0.6022 0 TD (B)Tj /F9 1 Tf 7.9701 0 0 7.9701 355.08 528.6 Tm (2)Tj /F3 1 Tf 11.9552 0 0 11.9552 359.76 530.4 Tm (,)Tj /F11 1 Tf 0.6022 0 TD (B)Tj /F9 1 Tf 7.9701 0 0 7.9701 375.84 528.6 Tm (3)Tj /F3 1 Tf 11.9552 0 0 11.9552 380.52 530.4 Tm (,)Tj /F11 1 Tf 0.6022 0 TD (B)Tj /F9 1 Tf 7.9701 0 0 7.9701 396.6 528.6 Tm (4)Tj /F3 1 Tf 11.9552 0 0 11.9552 401.4 530.4 Tm (.)Tj ET 129.745 456.24 m 129.745 456.24 l 129.745 458.587 127.841 460.492 125.494 460.492 c 123.147 460.492 121.242 458.587 121.242 456.24 c 121.242 453.893 123.147 451.988 125.494 451.988 c 127.841 451.988 129.745 453.893 129.745 456.24 c h 158.092 442.067 m 158.092 442.067 l 158.092 444.414 156.187 446.319 153.84 446.319 c 151.493 446.319 149.588 444.414 149.588 442.067 c 149.588 439.72 151.493 437.815 153.84 437.815 c 156.187 437.815 158.092 439.72 158.092 442.067 c h 186.438 456.24 m 186.438 456.24 l 186.438 458.587 184.533 460.492 182.186 460.492 c 179.839 460.492 177.935 458.587 177.935 456.24 c 177.935 453.893 179.839 451.988 182.186 451.988 c 184.533 451.988 186.438 453.893 186.438 456.24 c h 158.092 470.413 m 158.092 470.413 l 158.092 472.76 156.187 474.665 153.84 474.665 c 151.493 474.665 149.588 472.76 149.588 470.413 c 149.588 468.066 151.493 466.161 153.84 466.161 c 156.187 466.161 158.092 468.066 158.092 470.413 c h 129.296 454.339 m 150.037 443.968 l 157.643 443.968 m 178.384 454.339 l 178.384 458.142 m 157.643 468.512 l 150.037 468.512 m 129.296 458.141 l 153.84 446.319 m 153.84 466.161 l 158.092 498.76 m 158.092 498.76 l 158.092 501.107 156.187 503.011 153.84 503.011 c 151.493 503.011 149.588 501.107 149.588 498.76 c 149.588 496.413 151.493 494.508 153.84 494.508 c 156.187 494.508 158.092 496.413 158.092 498.76 c h 127.852 459.778 m 151.482 495.222 l 156.198 495.222 m 179.828 459.778 l 129.745 456.24 m 177.935 456.24 l 153.84 494.508 m 153.84 474.665 l 228.985 470.4 m 228.985 470.4 l 228.985 472.747 227.081 474.652 224.734 474.652 c 222.387 474.652 220.482 472.747 220.482 470.4 c 220.482 468.053 222.387 466.148 224.734 466.148 c 227.081 466.148 228.985 468.053 228.985 470.4 c h 257.332 456.227 m 257.332 456.227 l 257.332 458.574 255.427 460.479 253.08 460.479 c 250.733 460.479 248.828 458.574 248.828 456.227 c 248.828 453.88 250.733 451.975 253.08 451.975 c 255.427 451.975 257.332 453.88 257.332 456.227 c h 285.678 470.4 m 285.678 470.4 l 285.678 472.747 283.773 474.652 281.426 474.652 c 279.079 474.652 277.175 472.747 277.175 470.4 c 277.175 468.053 279.079 466.148 281.426 466.148 c 283.773 466.148 285.678 468.053 285.678 470.4 c h 257.332 484.573 m 257.332 484.573 l 257.332 486.92 255.427 488.825 253.08 488.825 c 250.733 488.825 248.828 486.92 248.828 484.573 c 248.828 482.226 250.733 480.321 253.08 480.321 c 255.427 480.321 257.332 482.226 257.332 484.573 c h 228.536 468.499 m 249.277 458.128 l 256.883 458.128 m 277.624 468.499 l 277.624 472.301 m 256.883 482.672 l 249.277 482.672 m 228.536 472.301 l 228.985 470.4 m 277.175 470.4 l 257.332 512.92 m 257.332 512.92 l 257.332 515.267 255.427 517.171 253.08 517.171 c 250.733 517.171 248.828 515.267 248.828 512.92 c 248.828 510.573 250.733 508.668 253.08 508.668 c 255.427 508.668 257.332 510.573 257.332 512.92 c h 257.332 427.88 m 257.332 427.88 l 257.332 430.227 255.427 432.132 253.08 432.132 c 250.733 432.132 248.828 430.227 248.828 427.88 c 248.828 425.533 250.733 423.629 253.08 423.629 c 255.427 423.629 257.332 425.533 257.332 427.88 c h 255.438 431.418 m 279.068 466.862 l 227.092 466.862 m 250.722 431.418 l 253.08 508.668 m 253.08 488.825 l 253.08 432.132 m 253.08 451.975 l 328.225 470.4 m 328.225 470.4 l 328.225 472.747 326.321 474.652 323.974 474.652 c 321.627 474.652 319.722 472.747 319.722 470.4 c 319.722 468.053 321.627 466.148 323.974 466.148 c 326.321 466.148 328.225 468.053 328.225 470.4 c h 356.572 456.227 m 356.572 456.227 l 356.572 458.574 354.667 460.479 352.32 460.479 c 349.973 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509.382 m 425.572 473.938 l 450.216 466.366 m 438.731 431.914 l 452.905 466.366 m 464.389 431.914 l 455.812 470.4 m 475.655 470.4 l 451.56 474.652 m 451.56 508.668 l 447.308 470.4 m 427.465 470.4 l S BT 11.9552 0 0 11.9552 192.96 389.4 Tm 0.0008 Tc [(Figure)-327(3:)-430.9(Be)4.2(ine)4.2(k)35(e)-347.1(g)-2(raphs)]TJ /F11 1 Tf 11.0813 0 TD 0 Tc (B)Tj /F9 1 Tf 7.9701 0 0 7.9701 334.32 387.6 Tm (5)Tj /F3 1 Tf 11.9552 0 0 11.9552 339 389.4 Tm (,)Tj /F11 1 Tf 0.6022 0 TD (B)Tj /F9 1 Tf 7.9701 0 0 7.9701 355.08 387.6 Tm (6)Tj /F3 1 Tf 11.9552 0 0 11.9552 359.76 389.4 Tm (,)Tj /F11 1 Tf 0.6022 0 TD (B)Tj /F9 1 Tf 7.9701 0 0 7.9701 375.84 387.6 Tm (7)Tj /F3 1 Tf 11.9552 0 0 11.9552 380.52 389.4 Tm (,)Tj /F11 1 Tf 0.6022 0 TD (B)Tj /F9 1 Tf 7.9701 0 0 7.9701 396.6 387.6 Tm (8)Tj /F3 1 Tf 11.9552 0 0 11.9552 401.4 389.4 Tm (.)Tj -26.0875 -2.3287 TD -0.0013 Tc (As)Tj /F11 1 Tf 1.4755 0 TD 0 Tc (G)Tj /F3 1 Tf 1.1141 0 TD -0.0016 Tc [(is)-358.4(cla)25.7(w)2.8(-)-6.8(f)-3.7(ree,)-363(it)-354.3(f)-3.7(o)-4.4(llo)25.7(ws)-348.3(f)-3.7(r)-3(o)-4.4(m)-350.9(Beinek)32.6(es)-368.4(T)2.8(heo)-4.4(r)-3(em)-361.3(1)-4.4(0)-355.8(tha)-4.4(t)]TJ /F11 1 Tf 23.8993 0 TD 0 Tc (G)Tj /F3 1 Tf 1.1242 0 TD 0.0008 Tc [(c)4.2(o)-2(n)31.9(t)-0.6(ains)-356(at)-341.9(le)4.2(as)5.4(t)-362(o)-2(ne)]TJ -29.0786 -1.2045 TD 0.0011 Tc [(of)-262(the)-266.5(e)4.5(igh)32.2(t)-271.3(graphs)]TJ /F11 1 Tf 8.1403 0 TD 0 Tc (B)Tj /F10 1 Tf 7.9701 0 0 7.9701 178.2 345.36 Tm (i)Tj /F11 1 Tf 11.9552 0 0 11.9552 181.56 347.16 Tm 0.1706 Tc (,i)Tj /F3 1 Tf 1.0539 0 TD 0.2728 Tc (=1)Tj /F11 1 Tf 1.5257 0 TD 0.1706 Tc [(,...)10(,)]TJ /F3 1 Tf 2.1982 0 TD 0 Tc (8)Tj /F11 1 Tf 0.4918 0 TD (,)Tj /F3 1 Tf 0.532 0 TD -0.0006 Tc [(sho)26.7(w)3.8(n)-270.6(i)-0.6(n)-270.6(F)-4(igure)-258.4(2)-274.4(and)-260.6(F)-4(igure)-268.3(3)6.6(,)-281.7(a)-3.4(s)-267(i)-0.6(nduced)-280.7(subgraphs.)]TJ -14.9658 -1.2045 TD [(The)-308.4(g)-3.4(raphs)]TJ /F11 1 Tf 5.119 0 TD 0 Tc (B)Tj /F9 1 Tf 7.9701 0 0 7.9701 142.08 330.96 Tm (7)Tj /F3 1 Tf 11.9552 0 0 11.9552 150.36 332.76 Tm 0.0009 Tc (and)Tj /F11 1 Tf 1.877 0 TD 0 Tc (B)Tj /F9 1 Tf 7.9701 0 0 7.9701 181.68 330.96 Tm (8)Tj /F3 1 Tf 11.9552 0 0 11.9552 189.96 332.76 Tm -0.0003 Tc [(ha)27(v)33.9(e)-318.1(v)33.9(e)3.1(rtices)-316.9(of)-293.5(degree)-308.1(5,)-301.4(so)-304.3(they)-307.4(cannot)-302.8(b)-29.4(e)-298(s)4.3(ubgraphs)-306.9(of)]TJ /F11 1 Tf 24.451 0 TD 0 Tc (G)Tj /F3 1 Tf 0.7729 0 TD 0.4216 Tc [(.A)422.9(l)421.6(s)426.2(o)418.8(,)]TJ /F11 1 Tf -35.0907 -1.2145 TD 0 Tc (G)Tj /F3 1 Tf 1.2346 0 TD 0.0008 Tc [(cannot)-472.4(c)4.2(on)31.9(tain)-459.9(an)31.9(y)-466.9(o)-2(f)-463(t)-0.6(he)-467.6(graphs)]TJ /F11 1 Tf 15.2969 0 TD 0 Tc (B)Tj /F9 1 Tf 7.9701 0 0 7.9701 278.52 316.44 Tm (5)Tj /F11 1 Tf 11.9552 0 0 11.9552 283.32 318.24 Tm 0.1706 Tc (,B)Tj /F9 1 Tf 7.9701 0 0 7.9701 297.48 316.44 Tm 0 Tc (6)Tj /F3 1 Tf 11.9552 0 0 11.9552 307.68 318.24 Tm 0.001 Tc [(s)5.6(i)1(nc)4.4(e)-477.4(e)4.4(ac)34.5(h)-469.8(o)-1.8(f)-462.8(t)-0.4(he)4.4(m)-468.8(h)2(as)-466.2(a)-463.6(p)2(air)-462.1(o)-1.8(f)-462.8(v)35.2(e)4.4(rtic)4.4(e)4.4(s)]TJ -19.7137 -1.2045 TD 0.0012 Tc [(of)-292(de)4.6(gre)4.6(e)-306.6(four)-291.3(w)5.6(h)2.2(os)5.8(e)-306.6(trans)5.8(p)-27.9(o)-1.6(s)5.8(i)1.2(tion)-298.9(is)-295.3(an)-288.9(automorphis)5.8(m)-308(of)]TJ /F11 1 Tf 24.6718 0 TD 0 Tc (B)Tj /F10 1 Tf 7.9701 0 0 7.9701 375.84 302.04 Tm (i)Tj /F3 1 Tf 11.9552 0 0 11.9552 379.2 303.84 Tm 0.0009 Tc [(,)-310.3(a)-1.9(nd)-289.2(th)32(us)-305.7(of)-292.3(an)32(y)-296.1(s)5.5(up)-28.2(e)4.3(r)-0.5(graph)]TJ -25.696 -1.2045 TD 0.0007 Tc [(of)-322.6(max)4.8(i)0.7(m)32.8(u)1.7(m)-338.6(d)1.7(egree)-337.2(4)-2.1(.)-430.9(T)5.1(his)-336(c)4.1(on)31.8(tradicts)-336(t)-0.7(he)-327.1(as)5.3(s)5.3(u)1.7(mption)-339.6(that)]TJ /F11 1 Tf 26.1874 0 TD 0 Tc (m)Tj /F3 1 Tf 0.8532 0 TD (\()Tj /F11 1 Tf 0.3814 0 TD (G)Tj /F3 1 Tf 0.7729 0 TD (\))Tj /F11 1 Tf 0.6625 0 TD (>)Tj /F3 1 Tf 1.0339 0 TD 0.0028 Tc (2.)Tj -28.4257 -1.2145 TD -0.0001 Tc [(It)-372.9(follo)27.2(ws)-366.9(that)]TJ /F11 1 Tf 6.5243 0 TD 0 Tc (G)Tj /F3 1 Tf 1.1342 0 TD 0.0011 Tc [(has)-375.7(t)-0.3(o)-363.1(c)4.5(on)32.2(tain)-369.3(at)-361.7(le)4.5(as)5.7(t)-381.7(o)-1.7(ne)-366.9(of)-362.4(the)-366.9(f)-1(our)-361.7(g)-1.7(raphs)]TJ /F11 1 Tf 20.0948 0 TD 0 Tc (B)Tj /F10 1 Tf 7.9701 0 0 7.9701 430.2 273.12 Tm (i)Tj /F11 1 Tf 11.9552 0 0 11.9552 433.56 274.92 Tm 0.1706 Tc (,i)Tj /F3 1 Tf 1.1242 0 TD 0.3531 Tc (=1)Tj /F11 1 Tf 1.606 0 TD 0 Tc (,)Tj /F3 1 Tf 0.4416 0 TD (2)Tj /F11 1 Tf 0.4918 0 TD (,)Tj /F3 1 Tf 0.4416 0 TD (3)Tj /F11 1 Tf 0.4918 0 TD (,)Tj /F3 1 Tf 0.4417 0 TD 0.0028 Tc [(4.)-539.2(W)85.4(e)]TJ -35.2818 -1.2045 TD -0.0005 Tc [(examine)-318.3(e)2.9(ac)33(h)-320.7(o)-3.3(f)-313.8(t)-1.9(hem)-309.7(a)-3.3(s)-307.1(i)-0.5(nduced)-330.8(subgraphs)-317.1(of)-303.7(the)-308.3(c)2.9(la)26.8(w-)-5.7(free)-318.3(graph)]TJ /F11 1 Tf 28.6064 0 TD 0 Tc (G)Tj /F3 1 Tf 1.074 0 TD -0.0021 Tc [(wit)-3.5(h)-322.3(\()]TJ /F11 1 Tf 3.4127 0 TD 0 Tc (G)Tj /F3 1 Tf 0.7729 0 TD 0.2825 Tc [(\)=)9.7(4)-31.5(a)279.7(n)283.5(d)]TJ /F11 1 Tf -33.866 -1.2145 TD 0 Tc (m)Tj /F3 1 Tf 0.8532 0 TD (\()Tj /F11 1 Tf 0.3814 0 TD (G)Tj /F3 1 Tf 0.7729 0 TD (\))Tj /F8 1 Tf 0.6725 0 TD ()Tj /F3 1 Tf 1.064 0 TD 0.0004 Tc [(4.)-461.3(It)-332.3(eas)5(ily)-336.8(turns)-336.3(o)-2.4(ut)-332.3(for)-332.3(e)3.8(v)34.6(e)3.8(ry)]TJ /F11 1 Tf 13.3999 0 TD 0 Tc (i)Tj /F3 1 Tf 0.6223 0 TD 0.2929 Tc (=1)Tj /F11 1 Tf 1.5458 0 TD 0 Tc (,)Tj /F3 1 Tf 0.4416 0 TD (2)Tj /F11 1 Tf 0.4918 0 TD (,)Tj /F3 1 Tf 0.4416 0 TD (3)Tj /F11 1 Tf 0.4918 0 TD (,)Tj /F3 1 Tf 0.4416 0 TD 0.0015 Tc [(4,)-319.7(that)-331.2(if)]TJ /F11 1 Tf 4.1153 0 TD 0 Tc (G)Tj /F3 1 Tf 1.1041 0 TD -0.0022 Tc [(co)-5(n)28.9(t)-3.6(a)-5(i)-2.2(ns)]TJ /F11 1 Tf 3.8443 0 TD 0 Tc (B)Tj /F10 1 Tf 7.9701 0 0 7.9701 447.72 244.2 Tm (i)Tj /F3 1 Tf 11.9552 0 0 11.9552 455.16 246 Tm 0.001 Tc [(as)-325.7(an)-329.3(induc)4.4(e)4.4(d)]TJ -32.0497 -1.2045 TD -0.0007 Tc [(subgraph,)-372.1(then)]TJ /F11 1 Tf 6.8053 0 TD 0 Tc (G)Tj /F3 1 Tf 1.1242 0 TD 0.001 Tc [(has)-355.8(t)-0.4(o)-343.1(c)4.4(on)32.1(tain)-359.4(a)-704.5(s)5.6(ubgraph)]TJ /F11 1 Tf 11.9445 0 TD 0 Tc (I)Tj /F10 1 Tf 7.9701 0 0 7.9701 314.76 229.8 Tm (i)Tj /F3 1 Tf 11.9552 0 0 11.9552 318.12 231.6 Tm -0.0002 Tc [(,)-361.6(c)3.2(alled)-360.6(a)]TJ /F12 1 Tf 4.2659 0 TD 0.0012 Tc [(b)49.7(a)-0.7(sic)-371.9(i)0.1(nit)5(i)0.1(al)-371.1(sub)49.7(g)-0.5(r)51.9(aph)]TJ /F3 1 Tf 8.9734 0 TD 0.5019 Tc [(.A)503.2(l)501.9(l)150.6(f)499.8(o)499.1(u)502.9(r)]TJ -33.8262 -1.2045 TD -0.0001 Tc [(basic)-327.9(i)-0.1(nitial)-331.3(subgraphs)-336.8(are)-327.9(p)0.9(resen)31(t)-1.5(ed)-340.4(in)-330.4(Figure)-328.3(4)7.1(.)]TJ 1.4655 -1.2145 TD -0.0011 Tc [(As)-277.6(a)-3.9(n)-281.2(exa)-3.9(m)0.9(ple,)-302.2(w)33.4(e)-278.8(describ)-30.2(e)-288.8(a)-274.9(m)0.9(etho)-34(d)-281.2(h)-0.1(o)26.2(w)-277.8(to)-274.9(o)-3.9(b)-0.1(ta)-3.9(in)]TJ /F11 1 Tf 22.2929 0 TD 0 Tc (I)Tj /F9 1 Tf 7.9701 0 0 7.9701 361.2 200.88 Tm (1)Tj /F3 1 Tf 11.9552 0 0 11.9552 369.24 202.68 Tm 0.0013 Tc [(\(s)5.9(e)4.7(e)-276.4(Figure)-276.4(5\).)-410.2(D)-4.5(e)4.7(n)2.3(ote)-276.4(t)-0.1(he)-266.3(v)35.5(e)4.7(r-)]TJ -24.8629 -1.2045 TD -0.0005 Tc [(tex)-257.4(s)4.1(et)-262.9(of)]TJ /F11 1 Tf 4.0752 0 TD 0 Tc (B)Tj /F9 1 Tf 7.9701 0 0 7.9701 129.6 186.48 Tm (1)Tj /F3 1 Tf 11.9552 0 0 11.9552 137.4 188.28 Tm 0.0028 Tc (as)Tj /F2 1 Tf 1.1242 0 TD 0 Tc ({)Tj /F11 1 Tf 0.5019 0 TD (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 163.44 186.48 Tm (0)Tj /F11 1 Tf 11.9552 0 0 11.9552 168.24 188.28 Tm 0.1706 Tc (,x)Tj /F9 1 Tf 7.9701 0 0 7.9701 180.12 186.48 Tm 0 Tc (1)Tj /F11 1 Tf 11.9552 0 0 11.9552 184.92 188.28 Tm 0.1706 Tc (,x)Tj /F9 1 Tf 7.9701 0 0 7.9701 196.8 186.48 Tm 0 Tc (2)Tj /F11 1 Tf 11.9552 0 0 11.9552 201.48 188.28 Tm 0.1706 Tc (,x)Tj /F9 1 Tf 7.9701 0 0 7.9701 213.36 186.48 Tm 0 Tc (3)Tj /F11 1 Tf 11.9552 0 0 11.9552 218.16 188.28 Tm 0.1706 Tc (,y)Tj /F9 1 Tf 7.9701 0 0 7.9701 229.2 186.48 Tm 0 Tc (1)Tj /F2 1 Tf 11.9552 0 0 11.9552 233.76 188.28 Tm (})Tj /F3 1 Tf 0.5019 0 TD 0.0004 Tc [(.)-411.1(T)4.8(he)-257.2(trans)5(p)-28.7(o)-2.4(s)5(i)0.4(tion)-259.6(of)-252.7(v)34.6(e)3.8(rtices)]TJ /F11 1 Tf 12.9682 0 TD 0 Tc (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 401.4 186.48 Tm (0)Tj /F11 1 Tf 11.9552 0 0 11.9552 406.2 188.28 Tm 0.1706 Tc (,x)Tj /F9 1 Tf 7.9701 0 0 7.9701 418.08 186.48 Tm 0 Tc (2)Tj /F3 1 Tf 11.9552 0 0 11.9552 425.76 188.28 Tm 0.0008 Tc [(is)-255.6(an)-249.2(automorphis)5.4(m)]TJ -29.5906 -1.2145 TD -0.0005 Tc [(w)3.9(i)-0.5(th)-350.8(motion)-350.8(2.)-502.4(Hence,)-371.9(one)-348.4(o)-3.3(f)-343.9(t)-1.9(hes)4.1(e)-358.5(t)28.2(w)34(o)-354.6(v)33.7(ertices)4.1(,)-381.9(s)4.1(a)26.8(y)]TJ /F11 1 Tf 22.9755 0 TD 0 Tc (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 353.28 171.96 Tm (0)Tj /F3 1 Tf 11.9552 0 0 11.9552 357.96 173.76 Tm 0.001 Tc [(,)-360.4(h)2(as)-345.7(to)-343.1(ha)28.3(v)35.2(e)-357(anothe)4.4(r)-351.7(n)2(e)4.4(i)1(gh)32.1(b)-28.1(o)-1.8(ur.)]TJ -23.9194 -1.2045 TD -0.0005 Tc 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0.0028 Tc (or)Tj /F11 1 Tf 1.2948 0 TD 0 Tc (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 283.56 610.08 Tm (3)Tj /F3 1 Tf 11.9552 0 0 11.9552 288.24 611.88 Tm 0.0002 Tc [(.)-722.5(W)2.5(ithout)-422.8(loss)-426.8(of)-413.5(generalit)28.9(y)84.6(,)-461.5(w)34.7(e)-428(join)]TJ /F11 1 Tf 16.5817 0 TD 0 Tc (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 493.08 610.08 Tm (4)Tj /F3 1 Tf 11.9552 0 0 11.9552 502.8 611.88 Tm -0.0022 Tc [(wit)-3.6(h)]TJ /F11 1 Tf -36.0346 -1.2145 TD 0 Tc (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 78.6 595.5601 Tm (3)Tj /F3 1 Tf 11.9552 0 0 11.9552 83.4 597.36 Tm 0.0013 Tc [(.)-540.7(A)2.6(gain,)-370.1(w)35.8(e)-366.7(ge)4.7(t)-361.5(a)-362.9(c)4.7(l)1.3(a)28.6(w)]TJ /F11 1 Tf 10.218 0 TD 0 Tc (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 212.16 595.5601 Tm (3)Tj /F3 1 Tf 11.9552 0 0 11.9552 216.96 597.36 Tm (;)Tj /F11 1 Tf 0.4416 0 TD (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 228.84 595.5601 Tm (4)Tj /F11 1 Tf 11.9552 0 0 11.9552 233.52 597.36 Tm 0.1706 Tc (,x)Tj /F9 1 Tf 7.9701 0 0 7.9701 245.4 595.5601 Tm 0 Tc (2)Tj /F11 1 Tf 11.9552 0 0 11.9552 250.2 597.36 Tm 0.1706 Tc (,y)Tj /F9 1 Tf 7.9701 0 0 7.9701 261.24 595.5601 Tm 0 Tc (1)Tj /F3 1 Tf 11.9552 0 0 11.9552 265.8 597.36 Tm -0.0007 Tc [(.)-542.7(I)1(f)-364.2(w)33.8(e)-378.7(a)-3.5(dded)-361.1(t)-2.1(he)-368.7(edge)]TJ /F11 1 Tf 10.208 0 TD 0 Tc (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 394.44 595.5601 Tm (4)Tj /F11 1 Tf 11.9552 0 0 11.9552 399.24 597.36 Tm (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 405.84 595.5601 Tm (2)Tj /F3 1 Tf 11.9552 0 0 11.9552 410.64 597.36 Tm 0.0008 Tc [(,)-370.6(w)35.3(e)-367.2(w)35.3(ould)-369.6(obtain)-359.6(t)29.5(w)35.3(o)]TJ -28.3258 -1.2045 TD -0.0012 Tc [(v)33(e)2.2(rtices)]TJ /F11 1 Tf 3.5532 0 TD 0 Tc (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 121.08 581.16 Tm (0)Tj /F11 1 Tf 11.9552 0 0 11.9552 125.88 582.96 Tm 0.1706 Tc (,x)Tj /F9 1 Tf 7.9701 0 0 7.9701 137.76 581.16 Tm 0 Tc (2)Tj /F3 1 Tf 11.9552 0 0 11.9552 146.52 582.96 Tm 0.0009 Tc [(of)-673.7(de)4.3(gre)4.3(e)-337(4)-343.2(w)5.3(ith)-339.4(e)4.3(q)5(u)1.9(al)-350.4(c)4.3(l)0.9(os)5.5(e)4.3(d)-349.4(ne)4.3(igh)32(b)-28.2(ourho)-32(o)-32(d)1.9(s)5.5(.)-470.9(He)4.3(nc)4.3(e)4.3(,)-350.4(the)4.3(i)0.9(r)-341.8(trans)5.5(p)-28.2(o)-1.9(s)5.5(i)0.9(tion)]TJ -6.2333 -1.2145 TD 0.0002 Tc [(w)34.7(o)-2.6(uld)-350.1(y)4.3(ield)-360.2(the)-347.7(m)2.2(otion)-350.1(o)-2.6(f)-343.2(t)-1.2(his)-346.5(g)-2.6(raph,)-351.1(and)-340.1(t)-1.2(h)31.3(u)1.2(s)-356.6(o)-2.6(f)-343.2(a)-2.6(n)31.3(y)-347(sup)-28.9(e)3.6(rgraph)]TJ /F11 1 Tf 28.6466 0 TD 0 Tc (G)Tj /F3 1 Tf 0.7729 0 TD 0.0012 Tc [(.)-500.7(I)2.9(t)-341.5(w)35.7(ould)-359.2(b)-27.9(e)-336.7(2,)-350.1(b)-27.9(e)4.6(-)]TJ -29.4195 -1.2045 TD -0.0031 Tc [(ca)-5.9(use)-300.8()-1.1(\()]TJ /F11 1 Tf 3.774 0 TD 0 Tc (G)Tj /F3 1 Tf 0.7729 0 TD -0.0017 Tc [(\))-274.1(=)-284.6(4)-4.5(.)-423.3(Theref)-3.8(o)-4.5(r)-3.1(e,)-302.8(w)32.8(e)-299.4(ha)25.6(v)32.5(e)-299.4(to)-285.6(a)-4.5(d)-0.7(d)-281.8(t)-3.1(he)-289.4(edg)-4.5(e)]TJ /F11 1 Tf 18.017 0 TD 0 Tc (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 348.36 552.24 Tm (4)Tj /F11 1 Tf 11.9552 0 0 11.9552 353.16 554.04 Tm (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 358.92 552.24 Tm (1)Tj /F3 1 Tf 11.9552 0 0 11.9552 363.6 554.04 Tm 0.0002 Tc [(,)-300.9(t)-1.2(h)31.3(u)1.2(s)-286.3(o)-2.6(btaining)-283.7(the)-287.5(i)0.2(nitial)-290.9(basic)]TJ -24.3911 -1.2045 TD -0.0002 Tc (subgraph)Tj /F11 1 Tf 4.2458 0 TD 0 Tc (I)Tj /F9 1 Tf 7.9701 0 0 7.9701 127.92 537.84 Tm (1)Tj /F3 1 Tf 11.9552 0 0 11.9552 132.72 539.64 Tm 0.0001 Tc [(.)-431.5(S)1.1(imilar)-332.6(a)-2.7(rgumen)31.2(ts)-336.6(lead)-330.2(to)-323.9(the)-327.7(o)-2.7(ther)-332.6(three)-327.7(i)0.1(nitial)-331.1(bas)4.7(i)0.1(c)-327.7(s)4.7(ubgraphs)]TJ /F11 1 Tf 28.767 0 TD 0 Tc (I)Tj /F9 1 Tf 7.9701 0 0 7.9701 481.8 537.84 Tm (2)Tj /F11 1 Tf 11.9552 0 0 11.9552 486.6 539.64 Tm 0.1706 Tc (,I)Tj /F9 1 Tf 7.9701 0 0 7.9701 497.04 537.84 Tm 0 Tc (3)Tj /F11 1 Tf 11.9552 0 0 11.9552 501.72 539.64 Tm 0.1706 Tc (,I)Tj /F9 1 Tf 7.9701 0 0 7.9701 512.16 537.84 Tm 0 Tc (4)Tj /F3 1 Tf 11.9552 0 0 11.9552 516.84 539.64 Tm (.)Tj ET 0.797 w 172.345 466.68 m 172.345 466.68 l 172.345 469.027 170.441 470.932 168.094 470.932 c 165.747 470.932 163.842 469.027 163.842 466.68 c 163.842 464.333 165.747 462.428 168.094 462.428 c 170.441 462.428 172.345 464.333 172.345 466.68 c h 200.692 452.507 m 200.692 452.507 l 200.692 454.854 198.787 456.759 196.44 456.759 c 194.093 456.759 192.188 454.854 192.188 452.507 c 192.188 450.16 194.093 448.255 196.44 448.255 c 198.787 448.255 200.692 450.16 200.692 452.507 c h 229.038 466.68 m 229.038 466.68 l 229.038 469.027 227.133 470.932 224.786 470.932 c 222.439 470.932 220.535 469.027 220.535 466.68 c 220.535 464.333 222.439 462.428 224.786 462.428 c 227.133 462.428 229.038 464.333 229.038 466.68 c h 200.692 480.853 m 200.692 480.853 l 200.692 483.2 198.787 485.105 196.44 485.105 c 194.093 485.105 192.188 483.2 192.188 480.853 c 192.188 478.506 194.093 476.601 196.44 476.601 c 198.787 476.601 200.692 478.506 200.692 480.853 c h 171.896 464.779 m 192.637 454.408 l 200.243 454.408 m 220.984 464.779 l 220.984 468.581 m 200.243 478.952 l 192.637 478.952 m 171.896 468.581 l 196.44 456.759 m 196.44 476.601 l 200.692 509.2 m 200.692 509.2 l 200.692 511.547 198.787 513.451 196.44 513.451 c 194.093 513.451 192.188 511.547 192.188 509.2 c 192.188 506.853 194.093 504.948 196.44 504.948 c 198.787 504.948 200.692 506.853 200.692 509.2 c h 170.452 470.218 m 194.082 505.662 l 198.798 505.662 m 222.428 470.218 l 229.038 438.334 m 229.038 438.334 l 229.038 440.681 227.133 442.585 224.786 442.585 c 222.439 442.585 220.535 440.681 220.535 438.334 c 220.535 435.987 222.439 434.082 224.786 434.082 c 227.133 434.082 229.038 435.987 229.038 438.334 c h 200.243 450.605 m 220.984 440.235 l 224.786 442.585 m 224.786 462.428 l 228.044 441.067 m 246.884 456.876 225.287 509.2 200.692 509.2 c S BT /F11 1 Tf 11.9552 0 0 11.9552 193.56 441.12 Tm (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 200.16 439.32 Tm (0)Tj /F11 1 Tf 11.9552 0 0 11.9552 230.4 435.48 Tm (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 237 433.68 Tm (4)Tj /F11 1 Tf 11.9552 0 0 11.9552 153.84 460.92 Tm (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 160.44 459.12 Tm (1)Tj /F11 1 Tf 11.9552 0 0 11.9552 193.56 486.48 Tm (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 200.16 484.68 Tm (2)Tj /F11 1 Tf 11.9552 0 0 11.9552 221.88 472.32 Tm (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 228.48 470.52 Tm (3)Tj /F11 1 Tf 11.9552 0 0 11.9552 182.28 503.52 Tm (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 188.04 501.72 Tm (1)Tj ET 328.212 466.68 m 328.212 466.68 l 328.212 469.027 326.307 470.932 323.96 470.932 c 321.613 470.932 319.709 469.027 319.709 466.68 c 319.709 464.333 321.613 462.428 323.96 462.428 c 326.307 462.428 328.212 464.333 328.212 466.68 c h 356.559 466.68 m 356.559 466.68 l 356.559 469.027 354.654 470.932 352.307 470.932 c 349.96 470.932 348.055 469.027 348.055 466.68 c 348.055 464.333 349.96 462.428 352.307 462.428 c 354.654 462.428 356.559 464.333 356.559 466.68 c h 384.905 466.68 m 384.905 466.68 l 384.905 469.027 383 470.932 380.653 470.932 c 378.306 470.932 376.401 469.027 376.401 466.68 c 376.401 464.333 378.306 462.428 380.653 462.428 c 383 462.428 384.905 464.333 384.905 466.68 c h 413.251 466.68 m 413.251 466.68 l 413.251 469.027 411.347 470.932 409 470.932 c 406.653 470.932 404.748 469.027 404.748 466.68 c 404.748 464.333 406.653 462.428 409 462.428 c 411.347 462.428 413.251 464.333 413.251 466.68 c h 399.078 495.026 m 399.078 495.026 l 399.078 497.373 397.173 499.278 394.826 499.278 c 392.479 499.278 390.575 497.373 390.575 495.026 c 390.575 492.679 392.479 490.775 394.826 490.775 c 397.173 490.775 399.078 492.679 399.078 495.026 c h 370.732 438.334 m 370.732 438.334 l 370.732 440.681 368.827 442.585 366.48 442.585 c 364.133 442.585 362.228 440.681 362.228 438.334 c 362.228 435.987 364.133 434.082 366.48 434.082 c 368.827 434.082 370.732 435.987 370.732 438.334 c h 328.212 466.68 m 348.055 466.68 l 356.559 466.68 m 376.401 466.68 l 384.905 466.68 m 404.748 466.68 l 407.098 470.483 m 396.728 491.224 l 392.925 491.224 m 382.555 470.483 l 390.879 493.447 m 327.908 468.259 l 362.942 440.692 m 327.498 464.322 l 364.579 442.136 m 354.208 462.877 l 368.382 442.136 m 378.752 462.877 l 370.018 440.692 m 405.462 464.322 l S BT /F11 1 Tf 11.9552 0 0 11.9552 370.68 432.6 Tm (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 377.28 430.8 Tm (0)Tj /F11 1 Tf 11.9552 0 0 11.9552 318.24 472.32 Tm (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 324.84 470.52 Tm (1)Tj /F11 1 Tf 11.9552 0 0 11.9552 349.44 470.88 Tm (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 356.04 469.08 Tm (2)Tj /F11 1 Tf 11.9552 0 0 11.9552 384.96 470.88 Tm (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 391.56 469.08 Tm (3)Tj /F11 1 Tf 11.9552 0 0 11.9552 414.72 469.44 Tm (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 421.32 467.64 Tm (4)Tj /F11 1 Tf 11.9552 0 0 11.9552 400.44 492.12 Tm (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 406.2 490.32 Tm (1)Tj /F3 1 Tf 11.9552 0 0 11.9552 145.32 413.88 Tm 0.0003 Tc [(Figure)-317.5(5:)-431.4(Ho)27.6(w)-336.6(w)34.8(e)-327.5(g)-2.5(et)-332.4(the)-327.5(b)1.3(asic)-327.5(initial)-330.9(s)4.9(ubgraph)]TJ /F11 1 Tf 20.7974 0 TD 0 Tc (I)Tj /F9 1 Tf 7.9701 0 0 7.9701 399.12 412.08 Tm (1)Tj /F3 1 Tf 11.9552 0 0 11.9552 407.76 413.88 Tm 0.0023 Tc (from)Tj /F11 1 Tf 2.3186 0 TD 0 Tc (B)Tj /F9 1 Tf 7.9701 0 0 7.9701 444.36 412.08 Tm (1)Tj /F3 1 Tf 11.9552 0 0 11.9552 449.04 413.88 Tm (.)Tj -30.0724 -2.3789 TD -0.0002 Tc [(The)-358.2(b)0.8(asic)-348.1(initial)-341.5(g)-3(raphs)]TJ /F11 1 Tf 10.5292 0 TD 0 Tc (I)Tj /F10 1 Tf 7.9701 0 0 7.9701 220.56 383.64 Tm (i)Tj /F11 1 Tf 11.9552 0 0 11.9552 223.92 385.44 Tm 0.1706 Tc (,i)Tj /F3 1 Tf 1.084 0 TD 0.303 Tc (=1)Tj /F11 1 Tf 1.5558 0 TD 0 Tc (,)Tj /F3 1 Tf 0.4416 0 TD (2)Tj /F11 1 Tf 0.4918 0 TD (,)Tj /F3 1 Tf 0.4416 0 TD (3)Tj /F11 1 Tf 0.4918 0 TD (,)Tj /F3 1 Tf 0.4416 0 TD -0.0014 Tc [(4)-4.2(,)-332.6(will)-352.7(b)-30.5(e)-349.3(co)-4.2(nsidered)-361.8(a)-4.2(s)-338.1(ro)-34.3(o)-4.2(t)-2.8(ed)-341.7(a)-4.2(t)-344.1(the)-349.3(v)32.8(ertex)]TJ /F11 1 Tf 19.3319 0 TD 0 Tc (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 520.8 383.64 Tm (0)Tj /F3 1 Tf 11.9552 0 0 11.9552 72 371.04 Tm -0.0016 Tc [(\(see)-289.3(F)-5(i)-1.6(g)-4.4(u)-0.6(re)-279.3(4)-4.4(\))-3(.)-423.2(A)-281.4(co)-4.4(nnected)-301.7(induced)-291.7(subg)-4.4(ra)-4.4(ph)]TJ /F11 1 Tf 19.864 0 TD 0 Tc (H)Tj /F3 1 Tf 1.1744 0 TD 0.001 Tc [(of)-553.2(the)-286.7(g)-1.8(raph)]TJ /F11 1 Tf 5.7213 0 TD 0 Tc (G)Tj /F3 1 Tf 1.0539 0 TD -0.0006 Tc [(is)-277.1(called)-290.7(a)-3.4(n)]TJ /F12 1 Tf 4.9785 0 TD 0.001 Tc [(initial)-311.1(g)-0.7(r)51.7(aph)]TJ /F3 1 Tf -32.7921 -1.2045 TD 0.0003 Tc [(if)-403.3(it)-402.6(can)-410.3(b)-28.8(e)-397.8(o)-2.5(btained)-410.3(f)-1.8(rom)-399.2(o)-2.5(ne)-397.8(of)-403.3(the)-407.8(b)1.3(asic)-407.8(initial)-401.2(g)-2.5(raphs)]TJ /F11 1 Tf 25.3042 0 TD 0 Tc (I)Tj /F10 1 Tf 7.9701 0 0 7.9701 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[(s)5(u)1.4(c)33.9(h)-299.7(that)-292.1(eac)33.9(h)-289.7(red)-289.7(v)34.6(ertex)-296.6(o)-2.4(uts)5(i)0.4(de)-297.3(the)-287.3(i)0.4(nitial)-280.7(graph)]TJ /F11 1 Tf 21.49 0 TD 0 Tc (H)Tj /F3 1 Tf 1.1744 0 TD -0.0008 Tc [(has)-287.3(a)-3.6(t)-283.3(m)1.2(ost)-293.3(t)-2.2(hree)-288.5(red)-290.9(n)0.2(eigh)30.3(b)-29.9(o)-3.6(urs.)]TJ -22.2528 -1.2045 TD 0.0002 Tc [(An)-360.2(initial)-351.1(s)4.8(ubgraph)]TJ /F11 1 Tf 8.7626 0 TD 0 Tc (H)Tj /F3 1 Tf 1.2346 0 TD 0.0021 Tc [(ro)-30.8(ote)5.5(d)-348.2(at)]TJ /F11 1 Tf 4.3261 0 TD 0 Tc (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 267.36 533.64 Tm (0)Tj /F3 1 Tf 11.9552 0 0 11.9552 276.36 535.44 Tm -0.0006 Tc [(is)-357.4(called)]TJ /F12 1 Tf 3.8042 0 TD 0.0018 Tc [(sy)5(mmet)5.6(r)2.3(ic)]TJ /F3 1 Tf 4.828 0 TD -0.0008 Tc [(if)-354.2(there)-358.8(e)2.6(xists)-367.6(a)-344.9(non-)-6(iden)30.3(tit)27.9(y)]TJ -25.726 -1.2145 TD 0.0006 Tc [(automorphis)5.2(m)]TJ /F11 1 Tf 6.5745 0 TD 0 Tc ()Tj /F2 1 Tf 1.064 0 TD ()Tj /F3 1 Tf 1.1041 0 TD 0.0001 Tc (Aut\()Tj /F11 1 Tf 2.0376 0 TD 0 Tc (H)Tj /F3 1 Tf 0.8933 0 TD -0.0001 Tc [(\))-413.1(s)4.5(uc)33.4(h)-430.7(t)-1.5(hat)]TJ /F11 1 Tf 5.3098 0 TD 0 Tc ()Tj /F3 1 Tf 0.6324 0 TD (\()Tj /F11 1 Tf 0.3814 0 TD (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 293.76 519.12 Tm (0)Tj /F3 1 Tf 11.9552 0 0 11.9552 298.44 520.92 Tm 0.4431 Tc (\)=)Tj /F11 1 Tf 2.0175 0 TD 0 Tc (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 329.16 519.12 Tm (0)Tj /F3 1 Tf 11.9552 0 0 11.9552 333.96 520.92 Tm 0.7127 Tc [(.I)714.4(f)]TJ /F11 1 Tf 2.0577 0 TD 0 Tc (H)Tj /F3 1 Tf 1.3049 0 TD 0.0008 Tc [(is)-426.2(an)-409.8(initial)-420.8(s)5.4(ubgraph)-429.8(that)-412.2(is)]TJ -25.2744 -1.2045 TD -0.0016 Tc [(no)-4.4(t)-384.4(s)3(ymmetric,)-413.1(then)-382(w)32.9(e)-389.7(co)-4.4(lo)-4.4(ur)]TJ /F11 1 Tf 13.6608 0 TD 0 Tc (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 241.92 504.72 Tm (0)Tj /F3 1 Tf 11.9552 0 0 11.9552 251.16 506.52 Tm [(and)-380.4(a)-2.8(ll)-381.4(four)-372.8(neigh)31.1(b)-29.1(ours)-386.9(red,)-391.5(w)4.4(h)1(ile)-388.1(the)-378(v)34.2(ertices)-396.9(of)-383.5(the)]TJ -14.986 -1.2045 TD -0.0009 Tc [(second)-311.1(sphere)-298.6(at)]TJ /F11 1 Tf 7.3072 0 TD 0 Tc (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 165.96 490.32 Tm (0)Tj /F3 1 Tf 11.9552 0 0 11.9552 174.24 492.12 Tm -0.0022 Tc [(white.)-443.9(Hence,)]TJ /F11 1 Tf 6.193 0 TD 0 Tc (H)Tj /F3 1 Tf 1.1844 0 TD -0.0007 Tc [(will)-291.8(b)-29.8(e)-298.4(xed)-300.8(b)30.4(y)-297.7(ev)33.5(ery)-307.8(a)-3.5(utomorphism)-309.9(of)-283.9(the)-298.4(g)-3.5(raph)]TJ /F11 1 Tf 21.239 0 TD 0 Tc (G)Tj /F3 1 Tf -37.1684 -1.2145 TD 0.001 Tc [(pre)4.4(s)5.6(e)4.4(r)-0.4(v)5.1(i)1(ng)-363.2(an)32.1(y)-356.3(c)4.4(olouring)-343.1(of)-693.7(v)35.2(e)4.4(rtic)4.4(e)4.4(s)-355.8(of)]TJ /F11 1 Tf 17.0434 0 TD 0 Tc (G)Tj /F3 1 Tf 1.1141 0 TD 0.0007 Tc [(s)5.3(a)-2.1(tis)5.3(f)-1.4(y)4.8(i)0.7(ng)-363.5(the)-347.2(p)1.7(rop)-28.4(e)4.1(rt)29.4(y)-346.5(t)-0.7(hat)]TJ /F11 1 Tf 12.2456 0 TD 0 Tc (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 442.08 475.8 Tm (0)Tj /F3 1 Tf 11.9552 0 0 11.9552 450.96 477.6 Tm -0.0009 Tc [(is)-357.7(the)-338.8(o)-3.7(nly)-358.2(r)-2.3(ed)]TJ -31.6984 -1.2045 TD -0.0002 Tc [(v)34(e)3.2(rtex)-337.4(o)-3(f)]TJ /F11 1 Tf 4.0752 0 TD 0 Tc (G)Tj /F3 1 Tf 1.1041 0 TD 0.0005 Tc [(w)4.9(i)0.5(th)-329.8(four)-322.1(red)-329.8(n)1.5(eigh)31.6(b)-28.6(o)-2.3(urs)5.1(.)]TJ /F1 1 Tf -5.1793 -1.7064 TD -0.0017 Tc [(Lemma)-419.3(13.)]TJ /F12 1 Tf 5.8819 0 TD -0.0509 Tc [(Le)-52.6(t)]TJ /F11 1 Tf 1.7064 0 TD 0 Tc (H)Tj /F12 1 Tf 1.2647 0 TD 0.0006 Tc [(b)49.1(e)-362.4(a)-372.7(s)-0.9(ymmetric)-372.5(initial)-361.7(g)-1.1(r)51.3(aph)-372.7(r)51.3(o)48.9(ote)49.1(d)-372.7(at)]TJ /F11 1 Tf 16.5616 0 TD 0 Tc (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 382.44 441 Tm (0)Tj /F12 1 Tf 11.9552 0 0 11.9552 387.24 442.8 Tm 0.513 Tc [(.T)510.4(h)511.1(e)511.3(n)]TJ /F11 1 Tf 3.3826 0 TD 0 Tc (H)Tj /F12 1 Tf 1.2647 0 TD 0.0015 Tc [(is)-361.3(isomorphic)-361.5(t)5.3(o)]TJ -31.0158 -1.2145 TD 0.0018 Tc [(one)-381.3(o)-0.1(f)-380.7(t)5.6(he)-391.3(fol)-49.3(l)0.9(owing)-371.3(t)5.6(welve)-381.3(g)0.1(r)52.5(aphs)]TJ /F11 1 Tf 14.9858 0 TD 0 Tc (H)Tj /F9 1 Tf 7.9701 0 0 7.9701 260.88 426.48 Tm (1)Tj /F12 1 Tf 11.9552 0 0 11.9552 265.56 428.28 Tm (,)Tj /F11 1 Tf 0.6926 0 TD (H)Tj /F9 1 Tf 7.9701 0 0 7.9701 283.56 426.48 Tm (2)Tj /F12 1 Tf 11.9552 0 0 11.9552 288.24 428.28 Tm (,)Tj /F11 1 Tf 0.7026 0 TD (H)Tj /F9 1 Tf 7.9701 0 0 7.9701 307.32 433.32 Tm (+)Tj -0.1204 -0.9937 TD (2)Tj /F12 1 Tf 11.9552 0 0 11.9552 314.28 428.28 Tm (,)Tj /F11 1 Tf 0.7026 0 TD (H)Tj /F9 1 Tf 7.9701 0 0 7.9701 332.4 426.48 Tm (3)Tj /F12 1 Tf 11.9552 0 0 11.9552 337.08 428.28 Tm (,)Tj /F11 1 Tf 0.6926 0 TD (H)Tj /F9 1 Tf 7.9701 0 0 7.9701 355.08 426.48 Tm (4)Tj /F12 1 Tf 11.9552 0 0 11.9552 359.76 428.28 Tm (,)Tj /F11 1 Tf 0.7026 0 TD (H)Tj /F9 1 Tf 7.9701 0 0 7.9701 377.88 426.48 Tm (5)Tj /F12 1 Tf 11.9552 0 0 11.9552 382.56 428.28 Tm (,)Tj /F11 1 Tf 0.6926 0 TD (H)Tj /F9 1 Tf 7.9701 0 0 7.9701 401.52 433.32 Tm (+)Tj -0.1205 -0.9937 TD (5)Tj /F12 1 Tf 11.9552 0 0 11.9552 408.6 428.28 Tm (,)Tj /F11 1 Tf 0.6926 0 TD (H)Tj /F9 1 Tf 7.9701 0 0 7.9701 426.6 426.48 Tm (6)Tj /F12 1 Tf 11.9552 0 0 11.9552 431.28 428.28 Tm (,)Tj /F11 1 Tf 0.7026 0 TD (H)Tj /F9 1 Tf 7.9701 0 0 7.9701 449.4 426.48 Tm (7)Tj /F12 1 Tf 11.9552 0 0 11.9552 454.08 428.28 Tm (,)Tj /F11 1 Tf 0.6926 0 TD (H)Tj /F9 1 Tf 7.9701 0 0 7.9701 472.08 426.48 Tm (8)Tj /F12 1 Tf 11.9552 0 0 11.9552 476.88 428.28 Tm (,)Tj /F11 1 Tf 0.6926 0 TD (H)Tj /F9 1 Tf 7.9701 0 0 7.9701 494.88 426.48 Tm (9)Tj /F12 1 Tf 11.9552 0 0 11.9552 499.56 428.28 Tm (,)Tj /F11 1 Tf 0.6926 0 TD (H)Tj /F9 1 Tf 7.9701 0 0 7.9701 518.52 433.32 Tm (+)Tj -0.1205 -0.9937 TD (9)Tj /F12 1 Tf 11.9552 0 0 11.9552 72 413.88 Tm 0.0007 Tc [(pr)51.4(esent)4.5(e)49.2(d)-342.4(i)-0.4(n)-352.7(F)-3.7(igur)51.4(e)]TJ /F3 1 Tf 8.562 0 TD 0 Tc (6)Tj /F12 1 Tf 0.4918 0 TD (.)Tj -9.0538 -2.4592 TD 0.0003 Tc [(Pr)51(o)48.6(o)-1.6(f.)]TJ /F3 1 Tf 3.0614 0 TD -0.0014 Tc [(R)-4.1(eca)-4.2(ll)-312.6(tha)-4.2(t)]TJ /F11 1 Tf 5.0387 0 TD 0 Tc (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 175.44 382.68 Tm (0)Tj /F3 1 Tf 11.9552 0 0 11.9552 183.84 384.48 Tm -0.0005 Tc [(is)-307.1(of)-313.8(degree)-308.3(4)-314.5(a)-3.3(nd)-300.6(its)-307.1(n)0.5(eigh)30.6(b)-29.6(o)-3.3(urs)-317.1(\()-1.9(i.e.)-311.7(i)-0.5(ts)-307.1(rst)-323.1(sphere\))-323.1(i)-0.5(nduce)-318.3(a)-304.5(path)]TJ /F11 1 Tf -9.3549 -1.2045 TD 0 Tc (P)Tj /F3 1 Tf 1.0439 0 TD (=)Tj /F11 1 Tf 1.0439 0 TD (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 103.56 368.28 Tm (1)Tj /F11 1 Tf 11.9552 0 0 11.9552 108.36 370.08 Tm (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 114.96 368.28 Tm (2)Tj /F11 1 Tf 11.9552 0 0 11.9552 119.64 370.08 Tm (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 126.24 368.28 Tm (3)Tj /F11 1 Tf 11.9552 0 0 11.9552 131.04 370.08 Tm (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 137.64 368.28 Tm (4)Tj /F3 1 Tf 11.9552 0 0 11.9552 142.44 370.08 Tm -0.0011 Tc [(.)-432.7(T)3.3(he)-328.9(v)33.1(e)2.3(rtices)-337.8(a)-3.9(t)-323.7(dista)-3.9(n)-0.1(ce)-328.9(2)-315.1(f)-3.2(ro)-3.9(m)]TJ /F11 1 Tf 14.3534 0 TD 0 Tc (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 320.64 368.28 Tm (0)Tj /F3 1 Tf 11.9552 0 0 11.9552 329.28 370.08 Tm -0.001 Tc [(\(i.e.)-322.2(i)-1(ts)-317.6(second)-331.3(sphere\))-333.7(w)3.4(ill)-332.2(b)-30.1(e)-318.8(denoted)]TJ -21.5204 -1.2145 TD -0.0311 Tc (by)Tj /F11 1 Tf 1.3149 0 TD 0 Tc (y)Tj /F10 1 Tf 7.9701 0 0 7.9701 93.48 353.76 Tm (j)Tj /F3 1 Tf 11.9552 0 0 11.9552 97.92 355.56 Tm 0.4216 Tc [(.L)420.3(e)425(t)]TJ /F11 1 Tf 2.3989 0 TD 0 Tc ()Tj /F3 1 Tf 0.9234 0 TD 0.0007 Tc [(b)-28.4(e)-277(a)-293.2(n)1.7(on-ide)4.1(n)31.8(t)-0.7(it)29.4(y)-296.3(a)-2.1(utomorphis)5.3(m)-288.4(of)]TJ /F11 1 Tf 15.056 0 TD 0 Tc (H)Tj /F3 1 Tf 1.1744 0 TD -0.0028 Tc [(suc)30.7(h)-302.9(t)-4.2(h)-1.8(a)-5.6(t)]TJ /F11 1 Tf 4.2458 0 TD 0 Tc ()Tj /F3 1 Tf 0.6324 0 TD (\()Tj /F11 1 Tf 0.3814 0 TD (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 401.16 353.76 Tm (0)Tj /F3 1 Tf 11.9552 0 0 11.9552 405.96 355.56 Tm 0.2825 Tc (\)=)Tj /F11 1 Tf 1.6963 0 TD 0 Tc (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 432.84 353.76 Tm (0)Tj /F3 1 Tf 11.9552 0 0 11.9552 437.64 355.56 Tm 0.0007 Tc [(.)-420.9(S)1.7(inc)4.1(e)-297(the)-287(i)0.7(mage)]TJ -30.5843 -1.2045 TD 0.0008 Tc [(of)-352.6(the)-357.2()1.8(rs)5.4(t)-362(s)5.4(phere)-367.2(of)-352.6(a)-363.4()1.8(x)4.9(e)4.2(d)-359.6(v)35(ertex)-376.5(i)0.8(s)-356(again)-349.5(i)0.8(ts)]TJ 20.426 0 TD -0.0003 Tc [(rs)4.3(t)-363.1(s)4.3(phere,)-381.7(w)34.2(e)-368.3(h)0.7(a)27(v)33.9(e)-368.3(t)28.4(w)34.2(o)-364.5(p)-29.4(o)-3.1(s)4.3(s)4.3(i)-0.3(bilities)-367.1(f)-2.4(or)]TJ -20.426 -1.2045 TD 0.0003 Tc [(the)-327.5(r)-1.1(ealization)-330(o)-2.5(f)-323(t)-1.1(he)-327.5(fact)-322.3(that)]TJ /F11 1 Tf 13.3296 0 TD 0 Tc ()Tj /F3 1 Tf 0.6324 0 TD (\()Tj /F11 1 Tf 0.3814 0 TD (P)Tj /F3 1 Tf 0.7729 0 TD 0.2624 Tc (\)=)Tj /F11 1 Tf 1.6863 0 TD 0 Tc (P)Tj /F3 1 Tf 0.7729 0 TD -0.0022 Tc [(.)-433.8(W)80.4(e)-330(s)2.4(ha)-5(ll)-333.4(co)-5(nsider)-344.9(these)-340.1(t)26.5(w)32.3(o)-336.3(ca)-5(ses)-338.9(s)2.4(epa)-5(r)-3.6(a)-5(t)-3.6(ely)82.2(.)]TJ /F1 1 Tf -16.1099 -1.2145 TD 0.0004 Tc [(Case)-540.5(A.)]TJ /F3 1 Tf 4.4666 0 TD -0.0009 Tc [(The)-469.3(a)-3.7(utomorphism)]TJ /F11 1 Tf 8.7526 0 TD 0 Tc ()Tj /F3 1 Tf 1.0941 0 TD 0.0002 Tc [(is)-456.9(not)-462.9(t)-1.2(he)-458.1(iden)31.3(tit)28.9(y)-467.5(on)-460.5(the)-458.1(p)1.2(ath)]TJ /F11 1 Tf 14.2832 0 TD 0 Tc (P)Tj /F3 1 Tf 0.7729 0 TD 0.4818 Tc [(,t)480.4(h)482.8(a)479(t)18.7(i)481.8(s)486.4(,)]TJ /F11 1 Tf 4.4365 0 TD 0 Tc ()Tj /F15 1 Tf 7.9701 0 0 7.9701 501.12 310.44 Tm (|)Tj /F10 1 Tf 0.3011 0 TD (P)Tj /F3 1 Tf 11.9552 0 0 11.9552 516.48 312.24 Tm (=)Tj -37.1789 -1.2045 TD (\()Tj /F11 1 Tf 0.3814 0 TD (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 83.16 296.04 Tm (1)Tj /F11 1 Tf 11.9552 0 0 11.9552 87.96 297.84 Tm (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 94.56 296.04 Tm (4)Tj /F3 1 Tf 11.9552 0 0 11.9552 99.36 297.84 Tm 0.0014 Tc (\)\()Tj /F11 1 Tf 0.7628 0 TD 0 Tc (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 115.08 296.04 Tm (2)Tj /F11 1 Tf 11.9552 0 0 11.9552 119.76 297.84 Tm (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 126.36 296.04 Tm (3)Tj /F3 1 Tf 11.9552 0 0 11.9552 131.16 297.84 Tm 0.0014 Tc (\).)Tj -3.483 -1.2145 TD -0.0006 Tc [(This)-407.6(condition)-401.1(implies)-407.6(t)-2(hat)-403.5(t)-2(he)-398.7(second)]TJ 17.2542 0 TD -0.001 Tc [(sphere)-409.1(con)30.1(t)-2.4(ains)-408(another)-393.9(v)33.2(ertex,)-432.6(sa)26.3(y)]TJ /F11 1 Tf 15.7787 0 TD 0 Tc (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 490.2 281.52 Tm (2)Tj /F3 1 Tf 11.9552 0 0 11.9552 494.88 283.32 Tm 0.4115 Tc [(,s)416.1(u)412.5(c)445(h)]TJ -35.3722 -1.2045 TD 0.0015 Tc (that)Tj /F11 1 Tf 2.1179 0 TD 0 Tc ()Tj /F3 1 Tf 0.6323 0 TD (\()Tj /F11 1 Tf 0.3814 0 TD (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 115.2 267.12 Tm (1)Tj /F3 1 Tf 11.9552 0 0 11.9552 119.76 268.92 Tm 0.2825 Tc (\)=)Tj /F11 1 Tf 1.6963 0 TD 0 Tc (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 145.8 267.12 Tm (2)Tj /F3 1 Tf 11.9552 0 0 11.9552 154.32 268.92 Tm -0.0017 Tc [(\(see)-329.5(F)-5.1(i)-1.7(g)-4.5(u)-0.7(re)-319.6(4)-315.7(a)-4.5(nd)-321.9(F)-5.1(i)-1.7(g)-4.5(u)-0.7(re)-319.6(6)-4.5(\))-3.1(.)-433.3(I)0(n)-321.9(c)1.7(o)-4.5(n)-0.7(sequence,)-353(the)-319.5(e)1.7(dg)-4.5(es)]TJ /F11 1 Tf 23.6883 0 TD 0 Tc (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 443.28 267.12 Tm (2)Tj /F11 1 Tf 11.9552 0 0 11.9552 447.96 268.92 Tm (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 454.56 267.12 Tm (1)Tj /F3 1 Tf 11.9552 0 0 11.9552 459.36 268.92 Tm (,)Tj /F11 1 Tf 0.5922 0 TD (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 472.2 267.12 Tm (2)Tj /F11 1 Tf 11.9552 0 0 11.9552 476.88 268.92 Tm (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 483.48 267.12 Tm (2)Tj /F3 1 Tf 11.9552 0 0 11.9552 492.12 268.92 Tm 0.0291 Tc [(be)32.5(l)29.1(o)26.3(n)30.1(g)]TJ -35.1413 -1.2045 TD 0.0014 Tc (to)Tj /F11 1 Tf 1.1944 0 TD 0 Tc (H)Tj /F3 1 Tf 0.8933 0 TD -0.0017 Tc 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445.609 744.36 l S 0.797 w 453.262 744.36 m 471.121 744.36 l 473.236 747.783 m 463.903 766.449 l 422.213 747.783 m 412.88 766.449 l 400.124 747.783 m 409.457 766.449 l 432.853 769.872 m 414.995 769.872 l 471.764 746.483 m 439.864 767.749 l S 2.551 w 460.48 766.449 m 451.147 747.783 l 433.496 720.971 m 401.596 742.237 l 434.969 722.271 m 425.636 740.937 l 438.391 722.271 m 447.725 740.937 l 440.507 769.872 m 458.365 769.872 l S 0.797 w 439.864 720.971 m 471.764 742.237 l S BT /F11 1 Tf 11.9552 0 0 11.9552 440.52 713.76 Tm 0 g (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 447.12 711.96 Tm (0)Tj /F11 1 Tf 11.9552 0 0 11.9552 393.24 734.16 Tm (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 399.84 732.36 Tm (1)Tj /F11 1 Tf 11.9552 0 0 11.9552 416.28 734.16 Tm (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 422.88 732.36 Tm (2)Tj /F11 1 Tf 11.9552 0 0 11.9552 448.08 734.16 Tm (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 454.68 732.36 Tm (3)Tj /F11 1 Tf 11.9552 0 0 11.9552 469.8 734.16 Tm (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 476.4 732.36 Tm (4)Tj /F11 1 Tf 11.9552 0 0 11.9552 467.28 767.4 Tm (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 473.04 765.6 Tm (1)Tj /F11 1 Tf 11.9552 0 0 11.9552 397.08 767.4 Tm (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 402.84 765.6 Tm (2)Tj /F11 1 Tf 11.9552 0 0 11.9552 431.52 759.72 Tm (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 437.28 757.92 Tm (3)Tj /F1 1 Tf 11.9552 0 0 11.9552 395.76 716.4 Tm (H)Tj /F18 1 Tf 7.9701 0 0 7.9701 406.32 714.6 Tm (3)Tj ET 1 0 0 rg 134.279 667.92 m 134.279 667.92 l 134.279 670.032 132.565 671.747 130.453 671.747 c 128.34 671.747 126.626 670.032 126.626 667.92 c 126.626 665.808 128.34 664.093 130.453 664.093 c 132.565 664.093 134.279 665.808 134.279 667.92 c b 159.791 667.92 m 159.791 667.92 l 159.791 670.032 158.076 671.747 155.964 671.747 c 153.852 671.747 152.138 670.032 152.138 667.92 c 152.138 665.808 153.852 664.093 155.964 664.093 c 158.076 664.093 159.791 665.808 159.791 667.92 c s 185.302 667.92 m 185.302 667.92 l 185.302 670.032 183.588 671.747 181.476 671.747 c 179.364 671.747 177.649 670.032 177.649 667.92 c 177.649 665.808 179.364 664.093 181.476 664.093 c 183.588 664.093 185.302 665.808 185.302 667.92 c b 210.814 667.92 m 210.814 667.92 l 210.814 670.032 209.1 671.747 206.987 671.747 c 204.875 671.747 203.161 670.032 203.161 667.92 c 203.161 665.808 204.875 664.093 206.987 664.093 c 209.1 664.093 210.814 665.808 210.814 667.92 c h 198.058 693.432 m 198.058 693.432 l 198.058 695.544 196.344 697.258 194.232 697.258 c 192.119 697.258 190.405 695.544 190.405 693.432 c 190.405 691.319 192.119 689.605 194.232 689.605 c 196.344 689.605 198.058 691.319 198.058 693.432 c s 172.547 693.432 m 172.547 693.432 l 172.547 695.544 170.832 697.258 168.72 697.258 c 166.608 697.258 164.893 695.544 164.893 693.432 c 164.893 691.319 166.608 689.605 168.72 689.605 c 170.832 689.605 172.547 691.319 172.547 693.432 c b 147.035 693.432 m 147.035 693.432 l 147.035 695.544 145.321 697.258 143.208 697.258 c 141.096 697.258 139.382 695.544 139.382 693.432 c 139.382 691.319 141.096 689.605 143.208 689.605 c 145.321 689.605 147.035 691.319 147.035 693.432 c b 172.547 642.408 m 172.547 642.408 l 172.547 644.521 170.832 646.235 168.72 646.235 c 166.608 646.235 164.893 644.521 164.893 642.408 c 164.893 640.296 166.608 638.582 168.72 638.582 c 170.832 638.582 172.547 640.296 172.547 642.408 c b 2.551 w 134.279 667.92 m 152.138 667.92 l 133.636 670.043 m 165.536 691.309 l 159.791 667.92 m 177.649 667.92 l S 0.797 w 185.302 667.92 m 203.161 667.92 l 205.276 671.343 m 195.943 690.009 l 154.253 671.343 m 144.92 690.009 l 132.164 671.343 m 141.497 690.009 l 164.893 693.432 m 147.035 693.432 l 203.804 670.043 m 171.904 691.309 l S 2.551 w 192.52 690.009 m 183.187 671.343 l 165.536 644.531 m 133.636 665.797 l 167.009 645.831 m 157.675 664.497 l 170.431 645.831 m 179.765 664.497 l 172.547 693.432 m 190.405 693.432 l S 0.797 w 146.522 695.345 m 159.402 702.781 178.038 702.781 190.918 695.345 c 171.904 644.531 m 203.804 665.797 l S BT /F11 1 Tf 11.9552 0 0 11.9552 172.56 637.2 Tm 0 g (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 179.16 635.4 Tm (0)Tj /F11 1 Tf 11.9552 0 0 11.9552 125.4 657.72 Tm (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 132 655.92 Tm (1)Tj /F11 1 Tf 11.9552 0 0 11.9552 148.32 657.72 Tm (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 154.92 655.92 Tm (2)Tj /F11 1 Tf 11.9552 0 0 11.9552 180.24 657.72 Tm (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 186.84 655.92 Tm (3)Tj /F11 1 Tf 11.9552 0 0 11.9552 201.96 657.72 Tm (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 208.56 655.92 Tm (4)Tj /F11 1 Tf 11.9552 0 0 11.9552 199.32 690.84 Tm (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 205.08 689.04 Tm (1)Tj /F11 1 Tf 11.9552 0 0 11.9552 129.24 690.84 Tm (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 135 689.04 Tm (2)Tj /F11 1 Tf 11.9552 0 0 11.9552 163.56 683.16 Tm (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 169.32 681.36 Tm (3)Tj /F1 1 Tf 11.9552 0 0 11.9552 127.92 639.84 Tm (H)Tj /F18 1 Tf 7.9701 0 0 7.9701 138.48 638.04 Tm (4)Tj ET 1 0 0 rg 268.319 667.92 m 268.319 667.92 l 268.319 670.032 266.605 671.747 264.493 671.747 c 262.38 671.747 260.666 670.032 260.666 667.92 c 260.666 665.808 262.38 664.093 264.493 664.093 c 266.605 664.093 268.319 665.808 268.319 667.92 c b 293.831 667.92 m 293.831 667.92 l 293.831 670.032 292.116 671.747 290.004 671.747 c 287.892 671.747 286.178 670.032 286.178 667.92 c 286.178 665.808 287.892 664.093 290.004 664.093 c 292.116 664.093 293.831 665.808 293.831 667.92 c b 319.342 667.92 m 319.342 667.92 l 319.342 670.032 317.628 671.747 315.516 671.747 c 313.404 671.747 311.689 670.032 311.689 667.92 c 311.689 665.808 313.404 664.093 315.516 664.093 c 317.628 664.093 319.342 665.808 319.342 667.92 c b 344.854 667.92 m 344.854 667.92 l 344.854 670.032 343.14 671.747 341.027 671.747 c 338.915 671.747 337.201 670.032 337.201 667.92 c 337.201 665.808 338.915 664.093 341.027 664.093 c 343.14 664.093 344.854 665.808 344.854 667.92 c b 319.342 693.432 m 319.342 693.432 l 319.342 695.544 317.628 697.258 315.516 697.258 c 313.404 697.258 311.689 695.544 311.689 693.432 c 311.689 691.319 313.404 689.605 315.516 689.605 c 317.628 689.605 319.342 691.319 319.342 693.432 c s 268.319 693.432 m 268.319 693.432 l 268.319 695.544 266.605 697.258 264.493 697.258 c 262.38 697.258 260.666 695.544 260.666 693.432 c 260.666 691.319 262.38 689.605 264.493 689.605 c 266.605 689.605 268.319 691.319 268.319 693.432 c b 293.831 693.432 m 293.831 693.432 l 293.831 695.544 292.116 697.258 290.004 697.258 c 287.892 697.258 286.178 695.544 286.178 693.432 c 286.178 691.319 287.892 689.605 290.004 689.605 c 292.116 689.605 293.831 691.319 293.831 693.432 c h 344.854 693.432 m 344.854 693.432 l 344.854 695.544 343.14 697.258 341.027 697.258 c 338.915 697.258 337.201 695.544 337.201 693.432 c 337.201 691.319 338.915 689.605 341.027 689.605 c 343.14 689.605 344.854 691.319 344.854 693.432 c s 306.587 642.408 m 306.587 642.408 l 306.587 644.521 304.872 646.235 302.76 646.235 c 300.648 646.235 298.933 644.521 298.933 642.408 c 298.933 640.296 300.648 638.582 302.76 638.582 c 304.872 638.582 306.587 640.296 306.587 642.408 c b 2.551 w 268.319 667.92 m 286.178 667.92 l 264.493 671.747 m 264.493 689.605 l 293.831 667.92 m 311.689 667.92 l S 0.797 w 319.342 667.92 m 337.201 667.92 l 338.322 670.626 m 318.222 690.726 l 290.004 671.747 m 290.004 689.605 l 267.198 670.626 m 287.298 690.726 l 268.319 693.432 m 286.178 693.432 l 341.027 689.605 m 341.027 671.747 l 337.201 693.432 m 319.342 693.432 l S 2.551 w 315.516 689.605 m 315.516 671.747 l 299.576 644.531 m 267.677 665.797 l 301.049 645.831 m 291.716 664.497 l 304.471 645.831 m 313.805 664.497 l S 0.797 w 305.944 644.531 m 337.844 665.797 l S [4.732 2.839 0 0 ]0 d 267.807 695.345 m 288.088 707.054 317.432 707.054 337.714 695.345 c S BT /F11 1 Tf 11.9552 0 0 11.9552 306.48 637.2 Tm 0 g (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 313.08 635.4 Tm (0)Tj /F11 1 Tf 11.9552 0 0 11.9552 259.32 657.72 Tm (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 265.92 655.92 Tm (1)Tj /F11 1 Tf 11.9552 0 0 11.9552 282.24 657.72 Tm (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 288.84 655.92 Tm (2)Tj /F11 1 Tf 11.9552 0 0 11.9552 314.16 657.72 Tm (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 320.76 655.92 Tm (3)Tj /F11 1 Tf 11.9552 0 0 11.9552 335.88 657.72 Tm (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 342.48 655.92 Tm (4)Tj /F11 1 Tf 11.9552 0 0 11.9552 302.76 693.36 Tm (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 308.52 691.5601 Tm (1)Tj /F11 1 Tf 11.9552 0 0 11.9552 250.44 690.84 Tm (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 256.2 689.04 Tm (3)Tj /F11 1 Tf 11.9552 0 0 11.9552 292.44 685.6801 Tm (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 298.2 683.88 Tm (2)Tj /F11 1 Tf 11.9552 0 0 11.9552 346.08 690.84 Tm (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 351.84 689.04 Tm (4)Tj /F1 1 Tf 11.9552 0 0 11.9552 261.84 639.84 Tm (H)Tj /F9 1 Tf 7.9701 0 0 7.9701 272.4 645.96 Tm -0.0065 Tc [(\(+)-8.6(\))]TJ /F18 1 Tf 0 -1.1443 TD 0 Tc (5)Tj ET 1 0 0 rg []0 d 402.239 667.92 m 402.239 667.92 l 402.239 670.032 400.525 671.747 398.413 671.747 c 396.3 671.747 394.586 670.032 394.586 667.92 c 394.586 665.808 396.3 664.093 398.413 664.093 c 400.525 664.093 402.239 665.808 402.239 667.92 c b 427.751 667.92 m 427.751 667.92 l 427.751 670.032 426.036 671.747 423.924 671.747 c 421.812 671.747 420.098 670.032 420.098 667.92 c 420.098 665.808 421.812 664.093 423.924 664.093 c 426.036 664.093 427.751 665.808 427.751 667.92 c b 453.262 667.92 m 453.262 667.92 l 453.262 670.032 451.548 671.747 449.436 671.747 c 447.324 671.747 445.609 670.032 445.609 667.92 c 445.609 665.808 447.324 664.093 449.436 664.093 c 451.548 664.093 453.262 665.808 453.262 667.92 c b 478.774 667.92 m 478.774 667.92 l 478.774 670.032 477.06 671.747 474.947 671.747 c 472.835 671.747 471.121 670.032 471.121 667.92 c 471.121 665.808 472.835 664.093 474.947 664.093 c 477.06 664.093 478.774 665.808 478.774 667.92 c b 453.262 693.432 m 453.262 693.432 l 453.262 695.544 451.548 697.258 449.436 697.258 c 447.324 697.258 445.609 695.544 445.609 693.432 c 445.609 691.319 447.324 689.605 449.436 689.605 c 451.548 689.605 453.262 691.319 453.262 693.432 c s 402.239 693.432 m 402.239 693.432 l 402.239 695.544 400.525 697.258 398.413 697.258 c 396.3 697.258 394.586 695.544 394.586 693.432 c 394.586 691.319 396.3 689.605 398.413 689.605 c 400.525 689.605 402.239 691.319 402.239 693.432 c b 427.751 693.432 m 427.751 693.432 l 427.751 695.544 426.036 697.258 423.924 697.258 c 421.812 697.258 420.098 695.544 420.098 693.432 c 420.098 691.319 421.812 689.605 423.924 689.605 c 426.036 689.605 427.751 691.319 427.751 693.432 c h 478.774 693.432 m 478.774 693.432 l 478.774 695.544 477.06 697.258 474.947 697.258 c 472.835 697.258 471.121 695.544 471.121 693.432 c 471.121 691.319 472.835 689.605 474.947 689.605 c 477.06 689.605 478.774 691.319 478.774 693.432 c s 440.507 642.408 m 440.507 642.408 l 440.507 644.521 438.792 646.235 436.68 646.235 c 434.568 646.235 432.853 644.521 432.853 642.408 c 432.853 640.296 434.568 638.582 436.68 638.582 c 438.792 638.582 440.507 640.296 440.507 642.408 c b 2.551 w 402.239 667.92 m 420.098 667.92 l 398.413 671.747 m 398.413 689.605 l 427.751 667.92 m 445.609 667.92 l S 0.797 w 453.262 667.92 m 471.121 667.92 l 472.242 670.626 m 452.142 690.726 l 423.924 671.747 m 423.924 689.605 l 401.118 670.626 m 421.218 690.726 l 402.239 693.432 m 420.098 693.432 l 474.947 689.605 m 474.947 671.747 l 471.121 693.432 m 453.262 693.432 l S 2.551 w 449.436 689.605 m 449.436 671.747 l 433.496 644.531 m 401.596 665.797 l 434.969 645.831 m 425.636 664.497 l 438.391 645.831 m 447.725 664.497 l S 0.797 w 439.864 644.531 m 471.764 665.797 l 401.547 695.626 m 420.829 709.128 452.531 709.128 471.813 695.626 c 427.392 695.049 m 440.778 701.291 458.094 701.291 471.479 695.049 c S 2.551 w 401.881 695.049 m 415.266 701.291 432.582 701.291 445.968 695.049 c S BT /F11 1 Tf 11.9552 0 0 11.9552 440.52 637.2 Tm 0 g (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 447.12 635.4 Tm (0)Tj /F11 1 Tf 11.9552 0 0 11.9552 393.24 657.72 Tm (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 399.84 655.92 Tm (1)Tj /F11 1 Tf 11.9552 0 0 11.9552 416.28 657.72 Tm (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 422.88 655.92 Tm (2)Tj /F11 1 Tf 11.9552 0 0 11.9552 448.08 657.72 Tm (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 454.68 655.92 Tm (3)Tj /F11 1 Tf 11.9552 0 0 11.9552 469.8 657.72 Tm (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 476.4 655.92 Tm (4)Tj /F11 1 Tf 11.9552 0 0 11.9552 438 688.3201 Tm (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 443.76 686.52 Tm (1)Tj /F11 1 Tf 11.9552 0 0 11.9552 384.36 690.84 Tm (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 390.12 689.04 Tm (3)Tj /F11 1 Tf 11.9552 0 0 11.9552 426.48 685.6801 Tm (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 432.24 683.88 Tm (2)Tj /F11 1 Tf 11.9552 0 0 11.9552 480 690.84 Tm (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 485.76 689.04 Tm (4)Tj /F1 1 Tf 11.9552 0 0 11.9552 395.76 639.84 Tm (H)Tj /F18 1 Tf 7.9701 0 0 7.9701 406.32 638.04 Tm (6)Tj ET 1 0 0 rg 0.797 w 134.279 591.36 m 134.279 591.36 l 134.279 593.472 132.565 595.187 130.453 595.187 c 128.34 595.187 126.626 593.472 126.626 591.36 c 126.626 589.248 128.34 587.533 130.453 587.533 c 132.565 587.533 134.279 589.248 134.279 591.36 c b 159.791 591.36 m 159.791 591.36 l 159.791 593.472 158.076 595.187 155.964 595.187 c 153.852 595.187 152.138 593.472 152.138 591.36 c 152.138 589.248 153.852 587.533 155.964 587.533 c 158.076 587.533 159.791 589.248 159.791 591.36 c b 185.302 591.36 m 185.302 591.36 l 185.302 593.472 183.588 595.187 181.476 595.187 c 179.364 595.187 177.649 593.472 177.649 591.36 c 177.649 589.248 179.364 587.533 181.476 587.533 c 183.588 587.533 185.302 589.248 185.302 591.36 c b 210.814 591.36 m 210.814 591.36 l 210.814 593.472 209.1 595.187 206.987 595.187 c 204.875 595.187 203.161 593.472 203.161 591.36 c 203.161 589.248 204.875 587.533 206.987 587.533 c 209.1 587.533 210.814 589.248 210.814 591.36 c b 198.058 616.872 m 198.058 616.872 l 198.058 618.984 196.344 620.698 194.232 620.698 c 192.119 620.698 190.405 618.984 190.405 616.872 c 190.405 614.759 192.119 613.045 194.232 613.045 c 196.344 613.045 198.058 614.759 198.058 616.872 c h 121.523 616.872 m 121.523 616.872 l 121.523 618.984 119.809 620.698 117.697 620.698 c 115.584 620.698 113.87 618.984 113.87 616.872 c 113.87 614.759 115.584 613.045 117.697 613.045 c 119.809 613.045 121.523 614.759 121.523 616.872 c s 147.035 616.872 m 147.035 616.872 l 147.035 618.984 145.321 620.698 143.208 620.698 c 141.096 620.698 139.382 618.984 139.382 616.872 c 139.382 614.759 141.096 613.045 143.208 613.045 c 145.321 613.045 147.035 614.759 147.035 616.872 c b 172.547 565.848 m 172.547 565.848 l 172.547 567.961 170.832 569.675 168.72 569.675 c 166.608 569.675 164.893 567.961 164.893 565.848 c 164.893 563.736 166.608 562.022 168.72 562.022 c 170.832 562.022 172.547 563.736 172.547 565.848 c b 2.551 w 134.279 591.36 m 152.138 591.36 l 128.741 594.783 m 119.408 613.449 l 159.791 591.36 m 177.649 591.36 l S 0.797 w 185.302 591.36 m 203.161 591.36 l 205.276 594.783 m 195.943 613.449 l 132.164 594.783 m 141.497 613.449 l 121.523 616.872 m 139.382 616.872 l S 2.551 w 192.52 613.449 m 183.187 594.783 l 165.536 567.971 m 133.636 589.237 l 167.009 569.271 m 157.675 587.937 l 170.431 569.271 m 179.765 587.937 l S 0.797 w 171.904 567.971 m 203.804 589.237 l S BT /F11 1 Tf 11.9552 0 0 11.9552 172.56 560.76 Tm 0 g (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 179.16 558.96 Tm (0)Tj /F11 1 Tf 11.9552 0 0 11.9552 125.4 581.16 Tm (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 132 579.36 Tm (1)Tj /F11 1 Tf 11.9552 0 0 11.9552 148.32 581.16 Tm (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 154.92 579.36 Tm (2)Tj /F11 1 Tf 11.9552 0 0 11.9552 180.24 581.16 Tm (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 186.84 579.36 Tm (3)Tj /F11 1 Tf 11.9552 0 0 11.9552 201.96 581.16 Tm (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 208.56 579.36 Tm (4)Tj /F11 1 Tf 11.9552 0 0 11.9552 181.56 614.28 Tm (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 187.32 612.48 Tm (1)Tj /F11 1 Tf 11.9552 0 0 11.9552 103.68 614.28 Tm (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 109.44 612.48 Tm (2)Tj /F11 1 Tf 11.9552 0 0 11.9552 148.32 614.28 Tm (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 154.08 612.48 Tm (3)Tj /F1 1 Tf 11.9552 0 0 11.9552 127.92 563.28 Tm (H)Tj /F18 1 Tf 7.9701 0 0 7.9701 138.48 561.48 Tm (7)Tj ET 1 0 0 rg 268.319 591.36 m 268.319 591.36 l 268.319 593.472 266.605 595.187 264.493 595.187 c 262.38 595.187 260.666 593.472 260.666 591.36 c 260.666 589.248 262.38 587.533 264.493 587.533 c 266.605 587.533 268.319 589.248 268.319 591.36 c b 293.831 591.36 m 293.831 591.36 l 293.831 593.472 292.116 595.187 290.004 595.187 c 287.892 595.187 286.178 593.472 286.178 591.36 c 286.178 589.248 287.892 587.533 290.004 587.533 c 292.116 587.533 293.831 589.248 293.831 591.36 c b 319.342 591.36 m 319.342 591.36 l 319.342 593.472 317.628 595.187 315.516 595.187 c 313.404 595.187 311.689 593.472 311.689 591.36 c 311.689 589.248 313.404 587.533 315.516 587.533 c 317.628 587.533 319.342 589.248 319.342 591.36 c b 344.854 591.36 m 344.854 591.36 l 344.854 593.472 343.14 595.187 341.027 595.187 c 338.915 595.187 337.201 593.472 337.201 591.36 c 337.201 589.248 338.915 587.533 341.027 587.533 c 343.14 587.533 344.854 589.248 344.854 591.36 c b 332.098 616.872 m 332.098 616.872 l 332.098 618.984 330.384 620.698 328.272 620.698 c 326.159 620.698 324.445 618.984 324.445 616.872 c 324.445 614.759 326.159 613.045 328.272 613.045 c 330.384 613.045 332.098 614.759 332.098 616.872 c h 255.563 616.872 m 255.563 616.872 l 255.563 618.984 253.849 620.698 251.737 620.698 c 249.624 620.698 247.91 618.984 247.91 616.872 c 247.91 614.759 249.624 613.045 251.737 613.045 c 253.849 613.045 255.563 614.759 255.563 616.872 c s 281.075 616.872 m 281.075 616.872 l 281.075 618.984 279.361 620.698 277.248 620.698 c 275.136 620.698 273.422 618.984 273.422 616.872 c 273.422 614.759 275.136 613.045 277.248 613.045 c 279.361 613.045 281.075 614.759 281.075 616.872 c b 306.587 565.848 m 306.587 565.848 l 306.587 567.961 304.872 569.675 302.76 569.675 c 300.648 569.675 298.933 567.961 298.933 565.848 c 298.933 563.736 300.648 562.022 302.76 562.022 c 304.872 562.022 306.587 563.736 306.587 565.848 c b 2.551 w 268.319 591.36 m 286.178 591.36 l 262.781 594.783 m 253.448 613.449 l 293.831 591.36 m 311.689 591.36 l S 0.797 w 319.342 591.36 m 337.201 591.36 l 339.316 594.783 m 329.983 613.449 l 266.204 594.783 m 275.537 613.449 l 255.563 616.872 m 273.422 616.872 l S 2.551 w 326.56 613.449 m 317.227 594.783 l 299.576 567.971 m 267.677 589.237 l 301.049 569.271 m 291.716 587.937 l 304.471 569.271 m 313.805 587.937 l S 0.797 w 305.944 567.971 m 337.844 589.237 l 281.075 616.872 m 324.445 616.872 l S 2.551 w 255.051 618.785 m 275.332 630.494 304.676 630.494 324.958 618.785 c S BT /F11 1 Tf 11.9552 0 0 11.9552 306.48 560.76 Tm 0 g (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 313.08 558.96 Tm (0)Tj /F11 1 Tf 11.9552 0 0 11.9552 259.32 581.16 Tm (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 265.92 579.36 Tm (1)Tj /F11 1 Tf 11.9552 0 0 11.9552 282.24 581.16 Tm (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 288.84 579.36 Tm (2)Tj /F11 1 Tf 11.9552 0 0 11.9552 314.16 581.16 Tm (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 320.76 579.36 Tm (3)Tj /F11 1 Tf 11.9552 0 0 11.9552 335.88 581.16 Tm (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 342.48 579.36 Tm (4)Tj /F11 1 Tf 11.9552 0 0 11.9552 333.36 614.28 Tm (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 339.12 612.48 Tm (1)Tj /F11 1 Tf 11.9552 0 0 11.9552 237.6 614.28 Tm (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 243.36 612.48 Tm (2)Tj /F11 1 Tf 11.9552 0 0 11.9552 279.72 607.92 Tm (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 285.48 606.12 Tm (3)Tj /F1 1 Tf 11.9552 0 0 11.9552 261.84 563.28 Tm (H)Tj /F18 1 Tf 7.9701 0 0 7.9701 272.4 561.48 Tm (8)Tj ET 1 0 0 rg 0.797 w 402.239 591.36 m 402.239 591.36 l 402.239 593.472 400.525 595.187 398.413 595.187 c 396.3 595.187 394.586 593.472 394.586 591.36 c 394.586 589.248 396.3 587.533 398.413 587.533 c 400.525 587.533 402.239 589.248 402.239 591.36 c b 427.751 591.36 m 427.751 591.36 l 427.751 593.472 426.036 595.187 423.924 595.187 c 421.812 595.187 420.098 593.472 420.098 591.36 c 420.098 589.248 421.812 587.533 423.924 587.533 c 426.036 587.533 427.751 589.248 427.751 591.36 c b 453.262 591.36 m 453.262 591.36 l 453.262 593.472 451.548 595.187 449.436 595.187 c 447.324 595.187 445.609 593.472 445.609 591.36 c 445.609 589.248 447.324 587.533 449.436 587.533 c 451.548 587.533 453.262 589.248 453.262 591.36 c b 478.774 591.36 m 478.774 591.36 l 478.774 593.472 477.06 595.187 474.947 595.187 c 472.835 595.187 471.121 593.472 471.121 591.36 c 471.121 589.248 472.835 587.533 474.947 587.533 c 477.06 587.533 478.774 589.248 478.774 591.36 c b 453.262 616.872 m 453.262 616.872 l 453.262 618.984 451.548 620.698 449.436 620.698 c 447.324 620.698 445.609 618.984 445.609 616.872 c 445.609 614.759 447.324 613.045 449.436 613.045 c 451.548 613.045 453.262 614.759 453.262 616.872 c h 389.483 616.872 m 389.483 616.872 l 389.483 618.984 387.769 620.698 385.657 620.698 c 383.544 620.698 381.83 618.984 381.83 616.872 c 381.83 614.759 383.544 613.045 385.657 613.045 c 387.769 613.045 389.483 614.759 389.483 616.872 c s 414.995 616.872 m 414.995 616.872 l 414.995 618.984 413.281 620.698 411.168 620.698 c 409.056 620.698 407.342 618.984 407.342 616.872 c 407.342 614.759 409.056 613.045 411.168 613.045 c 413.281 613.045 414.995 614.759 414.995 616.872 c b 478.774 616.872 m 478.774 616.872 l 478.774 618.984 477.06 620.698 474.947 620.698 c 472.835 620.698 471.121 618.984 471.121 616.872 c 471.121 614.759 472.835 613.045 474.947 613.045 c 477.06 613.045 478.774 614.759 478.774 616.872 c s 440.507 565.848 m 440.507 565.848 l 440.507 567.961 438.792 569.675 436.68 569.675 c 434.568 569.675 432.853 567.961 432.853 565.848 c 432.853 563.736 434.568 562.022 436.68 562.022 c 438.792 562.022 440.507 563.736 440.507 565.848 c b 2.551 w 402.239 591.36 m 420.098 591.36 l 396.701 594.783 m 387.368 613.449 l 427.751 591.36 m 445.609 591.36 l S 0.797 w 453.262 591.36 m 471.121 591.36 l 472.242 594.066 m 452.142 614.166 l 400.124 594.783 m 409.457 613.449 l 389.483 616.872 m 407.342 616.872 l 474.947 613.045 m 474.947 595.187 l 471.121 616.872 m 453.262 616.872 l S 2.551 w 449.436 613.045 m 449.436 595.187 l 433.496 567.971 m 401.596 589.237 l 434.969 569.271 m 425.636 587.937 l 438.391 569.271 m 447.725 587.937 l S 0.797 w 439.864 567.971 m 471.764 589.237 l S [5.069 3.041 0 0 ]0 d 388.971 618.785 m 412.953 632.631 447.652 632.631 471.634 618.785 c S [4.729 2.837 0 0 ]0 d 414.764 618.18 m 432.578 624.664 453.538 624.664 471.352 618.18 c S BT /F11 1 Tf 11.9552 0 0 11.9552 440.52 560.76 Tm 0 g (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 447.12 558.96 Tm (0)Tj /F11 1 Tf 11.9552 0 0 11.9552 393.24 581.16 Tm (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 399.84 579.36 Tm (1)Tj /F11 1 Tf 11.9552 0 0 11.9552 416.28 581.16 Tm (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 422.88 579.36 Tm (2)Tj /F11 1 Tf 11.9552 0 0 11.9552 448.08 581.16 Tm (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 454.68 579.36 Tm (3)Tj /F11 1 Tf 11.9552 0 0 11.9552 469.8 581.16 Tm (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 476.4 579.36 Tm (4)Tj /F11 1 Tf 11.9552 0 0 11.9552 438 610.44 Tm (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 443.76 608.64 Tm (1)Tj /F11 1 Tf 11.9552 0 0 11.9552 371.64 614.28 Tm (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 377.4 612.48 Tm (2)Tj /F11 1 Tf 11.9552 0 0 11.9552 413.64 610.44 Tm (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 419.4 608.64 Tm (3)Tj /F11 1 Tf 11.9552 0 0 11.9552 480 614.28 Tm (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 485.76 612.48 Tm (4)Tj /F1 1 Tf 11.9552 0 0 11.9552 395.76 563.28 Tm (H)Tj /F9 1 Tf 7.9701 0 0 7.9701 406.32 569.4 Tm -0.0065 Tc [(\(+)-8.6(\))]TJ /F18 1 Tf 0 -1.1292 TD 0 Tc (9)Tj /F3 1 Tf 11.9552 0 0 11.9552 72 541.44 Tm 0.0007 Tc [(Figure)-347.2(6:)-491.2(Initial)-350.6(s)5.3(y)4.8(mmetric)-377.3(s)5.3(ubgraphs)-356.1(w)5.1(i)0.7(th)-359.7(ad)]TJ 20.0446 0 TD -0.0002 Tc [(equate)-358.2(v)34(e)3.2(rtex)-367.5(c)3.2(olourings.)-522.2(Bold)-360.6(subgraphs)]TJ -20.0446 -1.2145 TD 0.0007 Tc [(are)-367.3(i)0.7(nduc)4.1(e)4.1(d)1.7(.)-601.6(A)-369.4(graph)-369.7(h)1.7(a)28(v)4.8(ing)-393.6(d)1.7(as)5.3(he)4.1(d)-379.7(e)4.1(dge)4.1(s)-386.2(s)5.3(t)-0.7(ands)-376.1(ac)4.1(tually)-376.6(for)-372.1(t)29.4(w)35.2(o)-383.6(graphs)5.3(,)-390.8(o)-2.1(ne)-367.3(w)5.1(i)0.7(thout)]TJ 0 -1.2045 TD -0.0009 Tc [(and)-331.2(t)-2.3(he)-328.7(second)-341.2(one)-318.7(w)3.5(ith)-341.2(d)0.1(ashed)-331.2(e)2.5(dges.)]TJ 1.4655 -2.8607 TD -0.0017 Tc (If)Tj /F11 1 Tf 1.1041 0 TD 0 Tc (H)Tj /F3 1 Tf 1.335 0 TD 0.0005 Tc [(is)-446.6(a)-454(s)5.1(up)-28.6(e)3.9(r)-0.9(graph)-450.2(o)-2.3(f)]TJ /F11 1 Tf 8.4916 0 TD 0 Tc (I)Tj /F9 1 Tf 7.9701 0 0 7.9701 225.36 476.52 Tm (4)Tj /F3 1 Tf 11.9552 0 0 11.9552 235.44 478.32 Tm 0.0006 Tc [(and)-450.1(t)-0.8(he)4(re)-447.7(is)-456.5(no)-443.9(additional)-451.1(e)4(d)1.6(ge)4(,)-481.2(t)-0.8(he)4(n)-460.1(w)35.1(e)-447.7(g)-2.2(e)4(t)]TJ /F11 1 Tf 20.3056 0 TD 0 Tc (H)Tj /F9 1 Tf 7.9701 0 0 7.9701 487.92 476.52 Tm (2)Tj /F3 1 Tf 11.9552 0 0 11.9552 492.6 478.32 Tm 0.803 Tc [(.T)807.4(h)804(e)]TJ -35.1814 -1.2045 TD 0.0013 Tc [(additional)-329.9(e)4.7(d)2.3(ge)]TJ /F11 1 Tf 6.8555 0 TD 0 Tc (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 159.72 462.12 Tm (1)Tj /F11 1 Tf 11.9552 0 0 11.9552 164.4 463.92 Tm (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 170.16 462.12 Tm (2)Tj /F3 1 Tf 11.9552 0 0 11.9552 178.68 463.92 Tm 0.0019 Tc [(c)35.4(h)2.9(ange)5.3(s)-334.8(i)1.9(t)-330.8(i)1.9(n)33(t)0.5(o)]TJ /F11 1 Tf 6.5945 0 TD 0 Tc (H)Tj /F9 1 Tf 7.9701 0 0 7.9701 268.2 468.84 Tm (+)Tj -0.1204 -0.9937 TD (2)Tj /F3 1 Tf 11.9552 0 0 11.9552 278.52 463.92 Tm (=)Tj /F11 1 Tf 1.0338 0 TD (H)Tj /F3 1 Tf 1.1141 0 TD (+)Tj /F11 1 Tf 0.9837 0 TD (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 321.72 462.12 Tm (1)Tj /F11 1 Tf 11.9552 0 0 11.9552 326.4 463.92 Tm (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 332.16 462.12 Tm (2)Tj /F3 1 Tf 11.9552 0 0 11.9552 336.84 463.92 Tm (.)Tj /F1 1 Tf -20.6873 -1.2145 TD 0.003 Tc [(S)5.7(u)5.7(b)-24.4(ca)7(s)4.4(e)-387.4(\(2\).)]TJ /F3 1 Tf 6.4741 0 TD -0.0014 Tc [(There)-339.3(a)-4.2(re)-319.2(exa)-4.2(c)2(tly)-338.6(t)-2.8(hree)-339.3(v)32.8(e)2(rtices)-338.1(in)-331.7(the)-329.2(s)3.2(eco)-4.2(nd)-341.7(sphere.)]TJ -6.4741 -1.2045 TD -0.0001 Tc [(Let)-312.7(u)0.9(s)-306.7(d)0.9(enote)-307.9(t)-1.5(his)-296.6(t)-1.5(hird)-310.3(v)34.1(e)3.3(rtex)-317.2(b)31(y)]TJ /F11 1 Tf 14.6846 0 TD 0 Tc (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 270.84 433.2 Tm (3)Tj /F3 1 Tf 11.9552 0 0 11.9552 275.52 435 Tm 0.0003 Tc [(.)-431.3(I)2(t)-302.2(i)0.3(s)-306.3(e)3.7(as)4.9(y)-306.8(t)-1.1(o)-303.7(s)4.9(ee)-307.5(that)-302.2(this)-306.3(v)34.5(e)3.7(rtex)-316.8(s)4.9(hould)-309.9(b)-28.8(e)-307.5()1.3(x)4.4(e)3.7(d)]TJ -17.0236 -1.2145 TD -0.0311 Tc (by)Tj /F11 1 Tf 1.355 0 TD 0 Tc ()Tj /F3 1 Tf 0.6324 0 TD -0.0014 Tc [(.)-433(S)-0.4(ince)-329.2(the)-329.2(v)32.8(ertices)]TJ /F11 1 Tf 8.4715 0 TD 0 Tc (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 203.64 418.68 Tm (2)Tj /F3 1 Tf 11.9552 0 0 11.9552 212.28 420.48 Tm 0.0009 Tc (and)Tj /F11 1 Tf 1.9071 0 TD 0 Tc (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 241.68 418.68 Tm (3)Tj /F3 1 Tf 11.9552 0 0 11.9552 250.32 420.48 Tm 0.0011 Tc [(are)-316.7(a)-1.7(lre)4.5(a)-1.7(dy)-326(of)-312.2(de)4.5(gre)4.5(e)-326.7(4,)-320.1(the)4.5(n)]TJ /F11 1 Tf 12.5366 0 TD 0 Tc (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 405.96 418.68 Tm (3)Tj /F3 1 Tf 11.9552 0 0 11.9552 414.48 420.48 Tm 0.0001 Tc [(has)-326.6(t)-1.3(o)-323.9(b)-29(e)-317.7(a)-2.7(ttac)33.6(h)1.1(ed)-330.1(b)31.2(y)]TJ -28.647 -1.2045 TD 0.0023 Tc [(an)-277.8(e)5.7(d)3.3(ge)-285.4(to)]TJ /F11 1 Tf 4.6573 0 TD 0 Tc (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 134.28 404.28 Tm (1)Tj /F3 1 Tf 11.9552 0 0 11.9552 142.44 406.08 Tm 0.0009 Tc (and)Tj /F11 1 Tf 1.8569 0 TD 0 Tc (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 171.24 404.28 Tm (4)Tj /F3 1 Tf 11.9552 0 0 11.9552 176.04 406.08 Tm -0.0003 Tc [(.)-421.9(N)1(ext,)-301.4(in)-280.4(order)-292.8(t)-1.7(o)-274.1(a)27(v)33.9(o)-3.1(id)-290.4(the)-288(c)3.1(la)27(w)]TJ /F11 1 Tf 14.4237 0 TD 0 Tc (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 355.08 404.28 Tm (1)Tj /F3 1 Tf 11.9552 0 0 11.9552 359.88 406.08 Tm (;)Tj /F11 1 Tf 0.4416 0 TD (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 370.92 404.28 Tm (3)Tj /F11 1 Tf 11.9552 0 0 11.9552 375.6 406.08 Tm 0.1706 Tc (,y)Tj /F9 1 Tf 7.9701 0 0 7.9701 386.64 404.28 Tm 0 Tc (2)Tj /F11 1 Tf 11.9552 0 0 11.9552 391.2 406.08 Tm 0.1706 Tc (,x)Tj /F9 1 Tf 7.9701 0 0 7.9701 403.08 404.28 Tm 0 Tc (0)Tj /F3 1 Tf 11.9552 0 0 11.9552 407.88 406.08 Tm 0.2894 Tc [(,w)323.9(eh)290.4(a)316.7(v)323.6(e)]TJ /F11 1 Tf 4.1755 0 TD 0 Tc (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 463.56 404.28 Tm (3)Tj /F11 1 Tf 11.9552 0 0 11.9552 468.24 406.08 Tm (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 474 404.28 Tm (2)Tj /F2 1 Tf 11.9552 0 0 11.9552 481.92 406.08 Tm ()Tj /F11 1 Tf 0.9435 0 TD (E)Tj /F3 1 Tf 0.7829 0 TD (\()Tj /F11 1 Tf 0.3814 0 TD (H)Tj /F3 1 Tf 0.8933 0 TD 0.0014 Tc (\).)Tj -37.2893 -1.2045 TD -0.0014 Tc [(By)-318.5(symmetry)83(,)-332.6(a)-4.2(lso)]TJ /F11 1 Tf 8.2306 0 TD 0 Tc (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 176.16 389.88 Tm (3)Tj /F11 1 Tf 11.9552 0 0 11.9552 180.84 391.68 Tm (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 186.6 389.88 Tm (1)Tj /F2 1 Tf 11.9552 0 0 11.9552 194.52 391.68 Tm ()Tj /F11 1 Tf 0.9435 0 TD (E)Tj /F3 1 Tf 0.7829 0 TD (\()Tj /F11 1 Tf 0.3814 0 TD (H)Tj /F3 1 Tf 0.8933 0 TD [(\),)-311.2(and)-320.2(w)34.5(e)-317.8(g)-2.8(et)-312.6(the)-317.8(g)-2.8(raph)]TJ /F11 1 Tf 10.3385 0 TD (H)Tj /F9 1 Tf 7.9701 0 0 7.9701 363.72 389.88 Tm (3)Tj /F3 1 Tf 11.9552 0 0 11.9552 372.12 391.68 Tm 0.0009 Tc [(\(s)5.5(e)4.3(e)-316.9(Figure)-306.9(6\).)-430.7(I)2.6(f)-312.4(a)-1.9(dditionally)85.3(,)]TJ -25.1038 -1.2145 TD 0.0006 Tc [(the)-347.3(e)4(dge)]TJ /F11 1 Tf 3.9547 0 TD 0 Tc (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 125.04 375.36 Tm (1)Tj /F11 1 Tf 11.9552 0 0 11.9552 129.72 377.16 Tm (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 135.48 375.36 Tm (2)Tj /F3 1 Tf 11.9552 0 0 11.9552 144.24 377.16 Tm 0.0012 Tc [(b)-27.9(e)4.6(longs)-345.5(t)-0.2(o)]TJ /F11 1 Tf 4.7477 0 TD 0 Tc (H)Tj /F3 1 Tf 0.8933 0 TD 0.3413 Tc [(,w)375.8(e)-6.6(g)338.5(e)344.7(t)]TJ /F11 1 Tf 3.7138 0 TD 0 Tc (H)Tj /F9 1 Tf 7.9701 0 0 7.9701 265.8 375.36 Tm (4)Tj /F3 1 Tf 11.9552 0 0 11.9552 270.6 377.16 Tm 0.4818 Tc [(.O)480(b)482.8(s)486.4(e)485.2(r)480.4(v)516(e)113.8(t)480.4(h)482.8(a)479(t)]TJ /F11 1 Tf 6.6748 0 TD 0 Tc (H)Tj /F9 1 Tf 7.9701 0 0 7.9701 360.12 375.36 Tm (3)Tj /F3 1 Tf 11.9552 0 0 11.9552 368.88 377.16 Tm 0.0009 Tc (and)Tj /F11 1 Tf 1.9171 0 TD 0 Tc (H)Tj /F9 1 Tf 7.9701 0 0 7.9701 401.52 375.36 Tm (4)Tj /F3 1 Tf 11.9552 0 0 11.9552 410.4 377.16 Tm 0.0009 Tc [(are)-337(s)5.5(up)-28.2(e)4.3(r)-0.5(graphs)-355.9(of)-342.5(the)]TJ -28.3058 -1.2045 TD 0.0015 Tc (graph)Tj /F11 1 Tf 2.7703 0 TD 0 Tc (I)Tj /F9 1 Tf 7.9701 0 0 7.9701 110.28 360.96 Tm (3)Tj /F3 1 Tf 11.9552 0 0 11.9552 118.92 362.76 Tm 0.0028 Tc (or)Tj /F11 1 Tf 1.2045 0 TD 0 Tc (I)Tj /F9 1 Tf 7.9701 0 0 7.9701 138.48 360.96 Tm (4)Tj /F3 1 Tf 11.9552 0 0 11.9552 143.16 362.76 Tm (.)Tj /F1 1 Tf -4.4868 -1.2045 TD 0.003 Tc [(S)5.7(u)5.7(b)-24.4(ca)7(s)4.4(e)-387.4(\(3\).)]TJ /F3 1 Tf 6.4741 0 TD -0.0006 Tc [(T)3.8(h)0.4(ere)-338.5(a)-3.4(re)-318.4(four)-333.3(v)33.6(e)2.8(rtices)-337.3(in)-330.9(the)-328.4(s)4(econd)-340.9(s)4(phere.)]TJ -6.4741 -1.2145 TD 0.0036 Tc [(De)7(n)4.6(o)0.8(te)-314.2(b)34.7(y)]TJ /F11 1 Tf 4.6975 0 TD 0 Tc (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 151.44 332.04 Tm (3)Tj /F3 1 Tf 11.9552 0 0 11.9552 159.96 333.84 Tm 0.0009 Tc (and)Tj /F11 1 Tf 1.887 0 TD 0 Tc (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 188.28 332.04 Tm (4)Tj /F3 1 Tf 11.9552 0 0 11.9552 196.68 333.84 Tm -0.001 Tc [(t)27.7(w)33.5(o)-335.1(n)0(ew)-317.8(v)33.2(e)2.4(rtices)-337.7(b)-30.1(e)2.4(longing)-315(t)-2.4(o)-315(t)-2.4(he)-318.8(second)-331.3(sphere)-328.8(and)-311.2(a)-3.8(djacen)30.1(t)-323.6(t)-2.4(o)]TJ /F11 1 Tf -10.429 -1.2045 TD 0 Tc (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 78.6 317.64 Tm (1)Tj /F3 1 Tf 11.9552 0 0 11.9552 87.96 319.44 Tm 0.0009 Tc (and)Tj /F11 1 Tf 1.9573 0 TD 0 Tc (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 117.96 317.64 Tm (4)Tj /F3 1 Tf 11.9552 0 0 11.9552 122.76 319.44 Tm -0.0025 Tc [(,)-394(r)-3.9(esp)-31.6(ectiv)31.7(ely)81.9(.)-634.9(Then)-403(a)-5.3(l)-2.5(so)]TJ /F11 1 Tf 11.1013 0 TD 0 Tc (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 261.24 317.64 Tm (3)Tj /F11 1 Tf 11.9552 0 0 11.9552 265.92 319.44 Tm (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 271.68 317.64 Tm (2)Tj /F2 1 Tf 11.9552 0 0 11.9552 280.8 319.44 Tm ()Tj /F11 1 Tf 1.0338 0 TD (E)Tj /F3 1 Tf 0.7829 0 TD (\()Tj /F11 1 Tf 0.3814 0 TD (H)Tj /F3 1 Tf 0.8933 0 TD -0.0008 Tc [(\).)-603.1(F)76.1(o)-3.6(r,)-382.2(w)33.7(e)-388.9(w)33.7(o)-3.6(uld)-401.3(h)0.2(a)26.5(v)33.4(e)-388.9(t)-2.2(he)-378.8(cla)26.5(w)-387.9(induced)]TJ -20.5568 -1.2145 TD -0.0311 Tc (by)Tj /F11 1 Tf 1.4052 0 TD 0 Tc (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 95.4 303.12 Tm (1)Tj /F3 1 Tf 11.9552 0 0 11.9552 100.2 304.92 Tm (;)Tj /F11 1 Tf 0.4416 0 TD (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 111.24 303.12 Tm (3)Tj /F11 1 Tf 11.9552 0 0 11.9552 115.92 304.92 Tm 0.1706 Tc (,y)Tj /F9 1 Tf 7.9701 0 0 7.9701 126.96 303.12 Tm 0 Tc (2)Tj /F11 1 Tf 11.9552 0 0 11.9552 131.52 304.92 Tm 0.1706 Tc (,x)Tj /F9 1 Tf 7.9701 0 0 7.9701 143.4 303.12 Tm 0 Tc (0)Tj /F3 1 Tf 11.9552 0 0 11.9552 148.2 304.92 Tm -0.0013 Tc [(.)-573.4(B)-0.9(y)-378.6(s)3.3(ymmetry)83.1(,)-402.8(a)-4.1(lso)]TJ /F11 1 Tf 9.2544 0 TD 0 Tc (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 264.6 303.12 Tm (1)Tj /F11 1 Tf 11.9552 0 0 11.9552 269.28 304.92 Tm (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 275.04 303.12 Tm (4)Tj /F2 1 Tf 11.9552 0 0 11.9552 284.04 304.92 Tm ()Tj /F11 1 Tf 1.0238 0 TD (E)Tj /F3 1 Tf 0.7829 0 TD (\()Tj /F11 1 Tf 0.3814 0 TD (H)Tj /F3 1 Tf 0.8933 0 TD 0.0013 Tc [(\).)-560.8(T)5.7(h)2.3(is)-375.5(graph)-369.1(i)1.3(s)-375.5(d)2.3(e)4.7(n)2.3(ote)4.7(d)-379.1(b)32.4(y)]TJ /F11 1 Tf 12.4965 0 TD 0 Tc (H)Tj /F9 1 Tf 7.9701 0 0 7.9701 480 303.12 Tm (5)Tj /F3 1 Tf 11.9552 0 0 11.9552 484.68 304.92 Tm 0.5721 Tc [(.I)573.8(t)189.3(c)575.5(a)569.3(n)]TJ -34.519 -1.2045 TD -0.0019 Tc [(b)-31(e)-420.1(co)-4.7(nsidered)-432.5(a)-4.7(s)-418.9(a)-426.3(s)2.7(up)-31(erg)-4.7(r)-3.3(a)-4.7(p)-0.9(h)-422.5(o)-4.7(f)]TJ /F11 1 Tf 14.8954 0 TD 0 Tc (I)Tj /F9 1 Tf 7.9701 0 0 7.9701 255.24 288.72 Tm (2)Tj /F3 1 Tf 11.9552 0 0 11.9552 265.08 290.52 Tm 0.0028 Tc (or)Tj /F11 1 Tf 1.2848 0 TD 0 Tc (I)Tj /F9 1 Tf 7.9701 0 0 7.9701 285.6 288.72 Tm (4)Tj /F3 1 Tf 11.9552 0 0 11.9552 290.28 290.52 Tm [(,)-441.7(a)-2.8(nd)-420.6(the)-418.2(s)4.6(ame)-428.2(a)-2.8(pplies)-427(t)-1.4(o)-414.4(t)-1.4(he)-418.2(graph)-420.6(w)4.4(ith)-420.6(a)-2.8(n)]TJ -18.2582 -1.2045 TD 0.0013 Tc [(additional)-329.9(e)4.7(d)2.3(ge)-326.5(b)-27.8(e)4.7(t)30(w)35.8(e)4.7(e)4.7(n)]TJ /F11 1 Tf 10.6295 0 TD 0 Tc (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 204.84 274.32 Tm (3)Tj /F11 1 Tf 11.9552 0 0 11.9552 209.52 276.12 Tm (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 215.28 274.32 Tm (4)Tj /F3 1 Tf 11.9552 0 0 11.9552 219.96 276.12 Tm -0.0001 Tc [(,)-331.3(i.e.)-441.8(t)-1.5(he)-327.9(graphs)]TJ /F11 1 Tf 7.1366 0 TD 0 Tc (H)Tj /F9 1 Tf 7.9701 0 0 7.9701 315.96 281.04 Tm (+)Tj -0.1205 -0.9937 TD (5)Tj /F3 1 Tf 11.9552 0 0 11.9552 326.28 276.12 Tm (=)Tj /F11 1 Tf 1.0439 0 TD (H)Tj /F9 1 Tf 7.9701 0 0 7.9701 348.48 274.32 Tm (5)Tj /F3 1 Tf 11.9552 0 0 11.9552 355.8 276.12 Tm (+)Tj /F11 1 Tf 0.9837 0 TD (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 373.32 274.32 Tm (3)Tj /F11 1 Tf 11.9552 0 0 11.9552 378 276.12 Tm (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 383.76 274.32 Tm (4)Tj /F3 1 Tf 11.9552 0 0 11.9552 388.44 276.12 Tm (.)Tj -25.0034 -1.2145 TD [(Ho)27.3(w)34.5(e)3.4(v)34.2(e)3.4(r,)-461.7(if)-423.7(w)34.5(e)-418.2(w)34.5(o)-2.8(uld)-430.6(lik)34.2(e)-418.2(t)-1.4(o)-414.4(a)-2.8(dd)-420.6(another)-413(e)3.4(dge)-428.2(t)-1.4(o)]TJ /F11 1 Tf 22.2428 0 TD (H)Tj /F9 1 Tf 7.9701 0 0 7.9701 365.16 259.8 Tm (5)Tj /F3 1 Tf 11.9552 0 0 11.9552 369.84 261.6 Tm 0.0014 Tc [(,)-440.3(e)4.8(.g.)]TJ /F11 1 Tf 2.8807 0 TD 0 Tc (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 410.04 259.8 Tm (3)Tj /F11 1 Tf 11.9552 0 0 11.9552 414.72 261.6 Tm (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 420.48 259.8 Tm (1)Tj /F3 1 Tf 11.9552 0 0 11.9552 425.16 261.6 Tm 0.4417 Tc [(,w)476.2(e)23.5(w)476.2(o)438.9(u)442.7(l)441.7(d)11.1(h)442.7(a)469(v)475.9(e)23.5(t)440.3(o)]TJ -29.5404 -1.2045 TD -0.0016 Tc [(co)-4.4(nsider)-304.1(a)-295.5(g)-4.4(ra)-4.4(ph)]TJ /F11 1 Tf 7.2972 0 TD 0 Tc (H)Tj /F3 1 Tf 1.1744 0 TD 0.001 Tc [(as)-285.5(a)-292.9(s)5.6(up)-28.1(e)4.4(r)-0.4(graph)-289.1(o)-1.8(f)-292.2(t)-0.4(he)-286.7(graph)]TJ /F11 1 Tf 12.4664 0 TD 0 Tc (I)Tj /F9 1 Tf 7.9701 0 0 7.9701 327.48 245.4 Tm (3)Tj /F3 1 Tf 11.9552 0 0 11.9552 335.64 247.2 Tm 0.0028 Tc (or)Tj /F11 1 Tf 1.1643 0 TD 0 Tc (I)Tj /F9 1 Tf 7.9701 0 0 7.9701 354.72 245.4 Tm (4)Tj /F3 1 Tf 11.9552 0 0 11.9552 359.4 247.2 Tm 0.0003 Tc [(.)-421.3(B)0.7(y)-296.7(s)4.9(y)4.4(mme)3.7(try)84.7(,)-320.9(o)-2.5(ur)-282.2(graph)-289.8(w)34.8(ould)]TJ -24.0398 -1.2045 TD -0.0006 Tc [(also)-334.7(ha)26.7(v)33.6(e)-348.5(the)-338.5(e)2.8(dge)]TJ /F11 1 Tf 8.1704 0 TD 0 Tc (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 175.44 231 Tm (2)Tj /F11 1 Tf 11.9552 0 0 11.9552 180.12 232.8 Tm (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 185.88 231 Tm (4)Tj /F3 1 Tf 11.9552 0 0 11.9552 190.56 232.8 Tm 0.3312 Tc [(,a)328.4(n)332.2(d)-9.1(a)328.4(l)331.2(s)335.8(o)]TJ /F11 1 Tf 4.4867 0 TD 0 Tc (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 249.96 231 Tm (3)Tj /F11 1 Tf 11.9552 0 0 11.9552 254.64 232.8 Tm (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 260.4 231 Tm (4)Tj /F3 1 Tf 11.9552 0 0 11.9552 269.16 232.8 Tm -0.0273 Tc [(t)-28.7(o)-361.4(av)6.9(o)-30.1(i)-27.3(d)-367.6(t)-28.7(h)-26.3(e)-365.2(c)-23.9(l)-27.3(aw)]TJ /F11 1 Tf 7.6987 0 TD 0 Tc (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 366.96 231 Tm (2)Tj /F3 1 Tf 11.9552 0 0 11.9552 371.64 232.8 Tm (;)Tj /F11 1 Tf 0.4416 0 TD (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 382.68 231 Tm (4)Tj /F11 1 Tf 11.9552 0 0 11.9552 387.36 232.8 Tm 0.1706 Tc (,y)Tj /F9 1 Tf 7.9701 0 0 7.9701 398.4 231 Tm 0 Tc (3)Tj /F11 1 Tf 11.9552 0 0 11.9552 402.96 232.8 Tm 0.1706 Tc (,x)Tj /F9 1 Tf 7.9701 0 0 7.9701 414.84 231 Tm 0 Tc (2)Tj /F3 1 Tf 11.9552 0 0 11.9552 419.64 232.8 Tm 0.0008 Tc [(.)-460.9(T)5.2(his)-335.9(w)35.3(a)28.1(y)-346.4(w)35.3(e)-337.1(arriv)35(e)]TJ -29.0786 -1.2145 TD 0.001 Tc [(at)-321.6(the)-326.8(g)-1.8(raph)]TJ /F11 1 Tf 5.6611 0 TD 0 Tc (H)Tj /F9 1 Tf 7.9701 0 0 7.9701 149.4 216.48 Tm (6)Tj /F3 1 Tf 11.9552 0 0 11.9552 154.08 218.28 Tm (.)Tj -5.4002 -1.2045 TD -0.0002 Tc [(Observ)34(e)-418.4(t)-1.6(hat)-393.1(t)-1.6(he)-398.3(edge)]TJ /F11 1 Tf 10.0775 0 TD 0 Tc (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 215.76 202.08 Tm (2)Tj /F11 1 Tf 11.9552 0 0 11.9552 220.44 203.88 Tm (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 226.2 202.08 Tm (1)Tj /F3 1 Tf 11.9552 0 0 11.9552 235.56 203.88 Tm -0.0007 Tc [(cannot)-403.6(b)-29.8(e)-388.8(a)-3.5(dded)-411.3(d)0.3(o)]TJ /F11 1 Tf 9.0637 0 TD 0 Tc (H)Tj /F9 1 Tf 7.9701 0 0 7.9701 353.64 202.08 Tm (5)Tj /F3 1 Tf 11.9552 0 0 11.9552 358.32 203.88 Tm 0.0001 Tc [(.)-642.3(F)77(or,)-411.4(e)3.5(ither)-402.8(w)34.6(e)-398(w)34.6(ould)-410.5(ha)27.4(v)34.3(e)-408(the)]TJ -23.9495 -1.2145 TD -0.0017 Tc [(cla)25.6(w)]TJ /F11 1 Tf 2.1781 0 TD 0 Tc (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 103.8 187.56 Tm (2)Tj /F3 1 Tf 11.9552 0 0 11.9552 108.48 189.36 Tm (;)Tj /F11 1 Tf 0.4416 0 TD (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 119.52 187.56 Tm (1)Tj /F11 1 Tf 11.9552 0 0 11.9552 124.2 189.36 Tm 0.1706 Tc (,y)Tj /F9 1 Tf 7.9701 0 0 7.9701 135.24 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[(\(2021\),)-370(#)2.2(P)6.8(3)-1.5(.)6.4(2)-1.5(5)-23835.6(1)-1.5(1)]TJ ET endstream endobj 53 0 obj << /ProcSet [/PDF /Text ] /Font << /F1 4 0 R /F2 5 0 R /F3 6 0 R /F6 9 0 R /F9 12 0 R /F11 14 0 R /F14 17 0 R /F18 54 0 R >> /ExtGState << /GS1 19 0 R >> >> endobj 58 0 obj << /Length 25876 >> stream BT /F3 1 Tf 11.9552 0 0 11.9552 72 757.92 Tm 0 g /GS1 gs 0.0008 Tc 0 Tw [(for,)-310.4(the)4.2(r)-0.6(e)-317(i)0.8(s)-315.8(o)-2(nly)-316.3(o)-2(ne)-317(e)4.2(d)1.8(ge)-307(going)-313.2(out)-321.8(o)-2(f)]TJ /F11 1 Tf 16.7825 0 TD 0 Tc (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 279.24 756.12 Tm (3)Tj /F3 1 Tf 11.9552 0 0 11.9552 287.88 757.92 Tm -0.0009 Tc [(to)-314.9(the)-308.7(s)3.7(econd)-331.2(sphere.)-452.6(T)3.5(his)-317.5(i)-0.9(mplies)-327.6(t)-2.3(hat)-313.5(i)-0.9(f)]TJ /F11 1 Tf 17.9568 0 TD 0 Tc (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 509.16 756.12 Tm (4)Tj /F3 1 Tf 11.9552 0 0 11.9552 517.6801 757.92 Tm (is)Tj -37.2793 -1.2045 TD -0.0011 Tc 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13.5504 0 TD 0 Tc (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 397.44 611.76 Tm (1)Tj /F11 1 Tf 11.9552 0 0 11.9552 402.12 613.5601 Tm (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 407.88 611.76 Tm (2)Tj /F3 1 Tf 11.9552 0 0 11.9552 415.92 613.5601 Tm (=)Tj /F11 1 Tf 1.0439 0 TD ()Tj /F3 1 Tf 0.6324 0 TD (\()Tj /F11 1 Tf 0.3814 0 TD (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 446.28 611.76 Tm (1)Tj /F11 1 Tf 11.9552 0 0 11.9552 450.96 613.5601 Tm (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 456.72 611.76 Tm (3)Tj /F3 1 Tf 11.9552 0 0 11.9552 461.4 613.5601 Tm 0.3327 Tc [(\)a)329.9(n)333.7(d)2.4(w)367.2(e)-5.2(g)329.9(e)336.1(t)]TJ -32.5717 -1.2145 TD 0 Tc [(a)-364.2(g)-2.8(raph)-360.4(isomorphic)-368(t)-1.4(o)]TJ /F11 1 Tf 9.8768 0 TD (H)Tj /F9 1 Tf 7.9701 0 0 7.9701 199.8 597.24 Tm (8)Tj /F3 1 Tf 11.9552 0 0 11.9552 204.6 599.04 Tm 0.0001 Tc [(.)-531.9(T)4.5(his)-366.7(t)-1.3(ime,)-381.3(ho)27.4(w)34.6(e)3.5(v)34.3(e)3.5(r,)-391.4(our)-362.7(g)-2.7(raph)-360.3(is)-366.7(not)-352.6(a)-364.1(sup)-29(e)3.5(rgraph)-370.3(of)]TJ /F11 1 Tf 24.19 0 TD 0 Tc (I)Tj /F9 1 Tf 7.9701 0 0 7.9701 498.96 597.24 Tm (2)Tj /F3 1 Tf 11.9552 0 0 11.9552 508.08 599.04 Tm -0.001 Tc (but)Tj -36.4763 -1.2045 TD 0.0028 Tc (of)Tj /F11 1 Tf 1.1141 0 TD 0 Tc (I)Tj /F9 1 Tf 7.9701 0 0 7.9701 90.48 582.84 Tm (3)Tj /F3 1 Tf 11.9552 0 0 11.9552 99.12 584.64 Tm 0.0028 Tc (or)Tj /F11 1 Tf 1.1944 0 TD 0 Tc (I)Tj /F9 1 Tf 7.9701 0 0 7.9701 118.56 582.84 Tm (4)Tj /F3 1 Tf 11.9552 0 0 11.9552 123.36 584.64 Tm (.)Tj -2.8306 -1.2145 TD 0.0007 Tc [(Finally)85.1(,)-330.5(i)0.7(f)]TJ /F11 1 Tf 4.4064 0 TD 0 Tc (H)Tj /F3 1 Tf 1.2045 0 TD -0.0006 Tc [(has)-317.2(a)-3.4(nother)-323.2(v)33.6(e)2.8(rtex)-337.8(a)-3.4(djacen)30.5(t)-323.2(t)-2(o)]TJ /F11 1 Tf 13.3697 0 TD 0 Tc (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 323.04 568.32 Tm (4)Tj /F3 1 Tf 11.9552 0 0 11.9552 327.84 570.12 Tm 0.3212 Tc [(,s)325.8(a)348.5(y)]TJ /F11 1 Tf 2.2785 0 TD 0 Tc (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 360.84 568.32 Tm (4)Tj /F3 1 Tf 11.9552 0 0 11.9552 365.52 570.12 Tm -0.0001 Tc [(,)-321.3(t)-1.5(hen)-320.3(i)-0.1(t)-322.7(a)-2.9(lso)-314.1(h)0.9(as)-316.7(the)-327.9(e)3.3(dge)]TJ /F11 1 Tf 11.3723 0 TD 0 Tc (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 507.24 568.32 Tm (1)Tj /F11 1 Tf 11.9552 0 0 11.9552 511.92 570.12 Tm (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 517.6801 568.32 Tm (4)Tj /F3 1 Tf 11.9552 0 0 11.9552 522.36 570.12 Tm (.)Tj -37.6707 -1.2045 TD -0.0008 Tc [(If)-324.1(w)33.7(e)-338.7(do)-324.8(not)-323.4(h)0.2(a)26.5(v)33.4(e)-338.7(a)-3.6(n)30.3(y)-327.9(other)-333.5(e)2.6(dges)-327.5(then)-341.1(w)33.7(e)-328.6(get)]TJ /F11 1 Tf 20.0847 0 TD 0 Tc (H)Tj /F9 1 Tf 7.9701 0 0 7.9701 321.84 553.92 Tm (9)Tj /F3 1 Tf 11.9552 0 0 11.9552 330.48 555.72 Tm 0.0002 Tc [(\(s)4.8(ee)-337.7(Figure)-317.7(6\).)-431.4(I)1.9(t)-332.5(i)0.2(s)-326.5(p)-28.9(os)4.8(s)4.8(i)0.2(ble,)-331(ho)27.5(w)34.7(e)3.6(v)34.4(e)3.6(r,)]TJ -21.6208 -1.2045 TD 0.0015 Tc (that)Tj /F11 1 Tf 2.2383 0 TD 0 Tc (H)Tj /F3 1 Tf 1.3249 0 TD -0.0021 Tc [(a)-4.9(l)-2.1(so)-446.6(ha)-4.9(s)-439.2(e)1.3(dg)-4.9(es)-449.2(co)-4.9(nnecting)]TJ /F11 1 Tf 11.6634 0 TD 0 Tc (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 259.8 539.52 Tm (4)Tj /F3 1 Tf 11.9552 0 0 11.9552 269.76 541.32 Tm -0.0022 Tc [(wit)-3.6(h)]TJ /F11 1 Tf 2.3387 0 TD 0 Tc (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 303.48 539.52 Tm (2)Tj /F3 1 Tf 11.9552 0 0 11.9552 313.44 541.32 Tm 0.0009 Tc (and)Tj /F11 1 Tf 2.0175 0 TD 0 Tc (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 343.32 539.52 Tm (3)Tj /F3 1 Tf 11.9552 0 0 11.9552 348 541.32 Tm 0.0009 Tc [(.)-772(T)5.3(he)4.3(n)-449.8(o)-1.9(ur)-432.1(graph)-439.8(t)-0.5(ak)35.1(e)4.3(s)-446.2(the)-437.4(f)-1.2(orm)]TJ -23.0863 -1.2145 TD 0.0028 Tc (of)Tj /F11 1 Tf 1.1744 0 TD 0 Tc (H)Tj /F9 1 Tf 7.9701 0 0 7.9701 96.72 531.72 Tm (+)Tj -0.1204 -0.9787 TD (9)Tj /F3 1 Tf 11.9552 0 0 11.9552 108.36 526.8 Tm (=)Tj /F11 1 Tf 1.1543 0 TD (H)Tj /F9 1 Tf 7.9701 0 0 7.9701 131.88 525 Tm (9)Tj /F3 1 Tf 11.9552 0 0 11.9552 139.68 526.8 Tm (+)Tj /F11 1 Tf 1.0338 0 TD (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 157.8 525 Tm (2)Tj /F11 1 Tf 11.9552 0 0 11.9552 162.48 526.8 Tm (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 168.24 525 Tm (4)Tj /F3 1 Tf 11.9552 0 0 11.9552 176.04 526.8 Tm (+)Tj /F11 1 Tf 1.0238 0 TD (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 194.04 525 Tm (3)Tj /F11 1 Tf 11.9552 0 0 11.9552 198.72 526.8 Tm (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 204.48 525 Tm (4)Tj /F11 1 Tf 11.9552 0 0 11.9552 209.16 526.8 Tm (.)Tj /F3 1 Tf 0.6625 0 TD 0.0013 Tc (Both)Tj /F11 1 Tf 2.4993 0 TD 0 Tc (H)Tj /F9 1 Tf 7.9701 0 0 7.9701 256.68 525 Tm (9)Tj /F3 1 Tf 11.9552 0 0 11.9552 266.04 526.8 Tm 0.0009 Tc (and)Tj /F11 1 Tf 1.9673 0 TD 0 Tc (H)Tj /F9 1 Tf 7.9701 0 0 7.9701 300.24 531.72 Tm (+)Tj -0.1205 -0.9787 TD (9)Tj /F3 1 Tf 11.9552 0 0 11.9552 311.88 526.8 Tm -0.0014 Tc [(ca)-4.2(n)-401.9(b)-30.5(e)-389.5(trea)-4.2(t)-2.8(ed)-391.9(a)-4.2(s)-388.3(g)-4.2(r)-2.8(a)-4.2(phs)-388.3(crea)-4.2(ted)-401.9(f)-3.5(ro)-4.2(m)]TJ /F11 1 Tf 17.0535 0 TD 0 Tc (I)Tj /F9 1 Tf 7.9701 0 0 7.9701 520.92 525 Tm (2)Tj /F3 1 Tf 11.9552 0 0 11.9552 72 512.4 Tm 0.0028 Tc (or)Tj /F11 1 Tf 1.1944 0 TD 0 Tc (I)Tj /F9 1 Tf 7.9701 0 0 7.9701 91.44 510.6 Tm (4)Tj /F3 1 Tf 11.9552 0 0 11.9552 96.24 512.4 Tm (.)Tj ET q 0.48 0 0 -7.92 517.068 520.308 cm /Im1 Do Q q 7.08 0 0 -0.48 517.548 520.308 cm /Im1 Do Q q 7.08 0 0 -0.48 517.548 512.868 cm /Im1 Do Q q 0.48 0 0 -7.92 524.5081 520.308 cm /Im1 Do Q BT 11.9552 0 0 11.9552 89.52 490.2 Tm -0.0011 Tc (Let)Tj /F11 1 Tf 1.7766 0 TD 0 Tc (H)Tj /F3 1 Tf 1.2246 0 TD 0.0004 Tc [(b)-28.7(e)-337.5(an)-339.9(initial)-350.9(s)5(ubgraph.)-481.4(If)]TJ /F11 1 Tf 11.2318 0 TD 0 Tc (H)Tj /F3 1 Tf 1.2346 0 TD -0.0013 Tc [(is)-338(s)3.3(y)2.8(mmetric,)-372.7(then)]TJ /F11 1 Tf 8.3009 0 TD 0 Tc (H)Tj /F3 1 Tf 1.2246 0 TD 0.0003 Tc [(is)-346.4(one)-337.6(o)-2.5(f)-343.1(t)-1.1(he)-337.6(t)29(w)34.8(e)3.7(l)0.3(v)34.5(e)-367.7(graphs)]TJ -26.4585 -1.2045 TD -0.0006 Tc [(sp)-29.7(ecied)-371(i)-0.6(n)-361(L)-1.9(emma)-364.9(13)6.6(.)-522.6(N)0.7(ote)-348.5(t)-2(hat)-353.3(t)-2(he)-358.6(graphs)]TJ /F11 1 Tf 19.8741 0 TD 0 Tc (H)Tj /F9 1 Tf 7.9701 0 0 7.9701 319.32 474 Tm (1)Tj /F3 1 Tf 11.9552 0 0 11.9552 328.32 475.8 Tm 0.0009 Tc (and)Tj /F11 1 Tf 1.9272 0 TD 0 Tc (H)Tj /F9 1 Tf 7.9701 0 0 7.9701 361.08 474 Tm (4)Tj /F3 1 Tf 11.9552 0 0 11.9552 370.08 475.8 Tm 0.0012 Tc [(are)-346.7(4)-1.6(-re)4.6(g)-1.6(ular,)-350.1(s)5.8(o)-363(n)2.2(one)-346.7(o)-1.6(f)-352.2(t)-0.2(he)4.6(m)]TJ -24.9332 -1.2145 TD 0.0002 Tc [(can)-400.3(b)-28.9(e)-397.9(a)-404.1(prop)-28.9(er)-402.7(subgraph)-400.3(of)-393.4(a)-404.1(g)-2.6(raph)]TJ /F11 1 Tf 16.6118 0 TD 0 Tc (G)Tj /F3 1 Tf 1.1643 0 TD -0.0021 Tc [(wit)-3.5(h)-412.7(\()]TJ /F11 1 Tf 3.503 0 TD 0 Tc (G)Tj /F3 1 Tf 0.7729 0 TD (\))Tj /F8 1 Tf 0.7829 0 TD ()Tj /F3 1 Tf 1.1844 0 TD 0.0028 Tc (4.)Tj /F11 1 Tf 1.4153 0 TD 0 Tc (H)Tj /F9 1 Tf 7.9701 0 0 7.9701 385.8 459.48 Tm (1)Tj /F3 1 Tf 11.9552 0 0 11.9552 395.28 461.28 Tm -0.0012 Tc [(is)-398.1(the)-399.3(c)2.2(o)-4(m)0.8(plemen)29.9(t)-424.2(o)-4(f)-404.8(t)-2.6(he)]TJ -27.041 -1.2045 TD -0.0027 Tc (cycle)Tj /F11 1 Tf 2.4692 0 TD 0 Tc (C)Tj /F9 1 Tf 7.9701 0 0 7.9701 109.92 445.08 Tm (7)Tj /F3 1 Tf 11.9552 0 0 11.9552 118.8 446.88 Tm (=)Tj /F11 1 Tf 1.1141 0 TD (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 138.72 445.08 Tm (0)Tj /F11 1 Tf 11.9552 0 0 11.9552 143.52 446.88 Tm (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 149.28 445.08 Tm (1)Tj /F11 1 Tf 11.9552 0 0 11.9552 153.96 446.88 Tm (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 160.56 445.08 Tm (2)Tj /F11 1 Tf 11.9552 0 0 11.9552 165.36 446.88 Tm (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 171.96 445.08 Tm (4)Tj /F11 1 Tf 11.9552 0 0 11.9552 176.76 446.88 Tm (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 183.36 445.08 Tm (1)Tj /F11 1 Tf 11.9552 0 0 11.9552 188.16 446.88 Tm (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 194.76 445.08 Tm (3)Tj /F11 1 Tf 11.9552 0 0 11.9552 199.56 446.88 Tm (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 205.32 445.08 Tm (2)Tj /F11 1 Tf 11.9552 0 0 11.9552 210 446.88 Tm (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 216.6 445.08 Tm (0)Tj /F3 1 Tf 11.9552 0 0 11.9552 225.72 446.88 Tm 0.001 Tc [(and)-379.4(i)1(t)-371.8(i)1(s)-365.8(e)4.4(as)5.6(y)-376.3(t)-0.4(o)-373.2(s)5.6(e)4.4(e)-377(that)-371.8(the)-367(c)4.4(olouring)-383.3(s)5.6(h)2(o)28.3(w)5.4(n)-379.4(i)1(n)-369.4(F)-2.4(igure)-367.3(6)]TJ -12.858 -1.2045 TD -0.0012 Tc [(sta)-4(b)-0.2(ilizes)-337.9(this)-337.9(cycle)-339.1(\()-2.6(a)-4(n)-0.2(d)-321.4(t)-2.6(h)29.9(u)-0.2(s)-337.9(i)-1.2(ts)-327.9(co)-4(mplemen)29.9(t\).)]TJ 1.4655 -1.2145 TD 0.0006 Tc [(As)-316(for)]TJ /F11 1 Tf 2.9209 0 TD 0 Tc (H)Tj /F9 1 Tf 7.9701 0 0 7.9701 134.16 416.16 Tm (4)Tj /F3 1 Tf 11.9552 0 0 11.9552 138.84 417.96 Tm 0.3212 Tc [(,o)318.4(b)322.2(s)325.8(e)324.6(r)319.8(v)355.4(e)-6.6(t)319.8(h)322.2(a)318.4(t)]TJ /F11 1 Tf 6.183 0 TD 0 Tc (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 219.36 416.16 Tm (2)Tj /F3 1 Tf 11.9552 0 0 11.9552 227.88 417.96 Tm -0.0002 Tc [(is)-316.8(the)-318(o)-3(nly)-317.3(w)4.2(hite)-318(v)34(e)3.2(rtex)-327.3(w)4.2(ith)-320.4(f)-2.3(our)-312.8(r)-1.6(ed)-320.4(neigh)30.9(b)-29.3(ours)-326.9(inducing)]TJ -13.0387 -1.2045 TD 0.2237 Tc [(ap)224.7(a)220.9(t)222.3(h)]TJ /F11 1 Tf 2.9008 0 TD 0 Tc (P)Tj /F9 1 Tf 7.9701 0 0 7.9701 114.24 401.76 Tm (4)Tj /F3 1 Tf 11.9552 0 0 11.9552 118.92 403.56 Tm -0.0006 Tc [(.)-402.1(T)3.8(his)-236.9(v)33.6(ertex)-237.4(a)-3.4(nd)-220.4(its)-226.9(n)0.4(eigh)30.5(b)-29.7(o)-3.4(urs)-236.9(a)-3.4(re)-218(xed)-240.5(b)-29.7(ecause)-228.1(t)-2(he)-228.1(path)]TJ /F11 1 Tf 24.6718 0 TD 0 Tc (P)Tj /F9 1 Tf 7.9701 0 0 7.9701 421.44 401.76 Tm (4)Tj /F3 1 Tf 11.9552 0 0 11.9552 428.76 403.56 Tm -0.0022 Tc [(ca)-5(nno)-5(t)-234.5(b)-31.3(e)-229.7(r)-3.6(ev)32(ersed.)]TJ -29.8415 -1.2145 TD -0.0011 Tc [(Indeed,)-272.1(t)-2.5(he)-248.6(end-)-6.3(v)33.1(e)2.3(rtices)-257.5(of)]TJ /F11 1 Tf 11.3221 0 TD 0 Tc (P)Tj /F9 1 Tf 7.9701 0 0 7.9701 214.92 387.24 Tm (4)Tj /F3 1 Tf 11.9552 0 0 11.9552 222.48 389.04 Tm -0.0006 Tc [(ha)26.7(v)33.6(e)-248.1(dieren)30.5(t)-253(n)30.5(u)0.4(m)31.5(b)-29.7(ers)-257(o)-3.4(f)-243.6(w)3.8(hite)-238.1(neigh)30.5(b)-29.7(ours.)-422.2(T)3.8(hen)-250.6(i)-0.6(t)-242.9(i)-0.6(s)-247(e)2.8(asily)]TJ -12.587 -1.2045 TD -0.0017 Tc [(seen)-342(tha)-4.5(t)-324.3(a)-4.5(l)-1.7(so)-335.8(the)-329.5(r)-3.1(ema)-4.5(i)-1.7(ning)-335.8(v)32.5(e)1.7(rtices)-348.4(o)-4.5(f)-325(the)-329.5(s)2.9(eco)-4.5(nd)-342(sphere)-339.6(a)-4.5(t)]TJ /F11 1 Tf 26.2176 0 TD 0 Tc (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 392.04 372.84 Tm (2)Tj /F3 1 Tf 11.9552 0 0 11.9552 400.8 374.64 Tm -0.0005 Tc [(cannot)-323.1(b)-29.6(e)-328.3(p)-29.6(erm)31.6(u)0.5(ted.)]TJ -26.0373 -1.2045 TD 0.0011 Tc [(T)5.5(h)2.1(is)-436(re)4.5(as)5.7(oning)-443.4(c)4.5(an)-429.5(b)-28(e)-427.1(re)4.5(p)-28(e)4.5(ate)4.5(d)-429.5(in)-429.5(the)-437.2(c)4.5(as)5.7(e)-427.1(o)-1.7(f)-432.6(g)-1.7(raphs)]TJ /F11 1 Tf 23.9291 0 TD 0 Tc (H)Tj /F9 1 Tf 7.9701 0 0 7.9701 385.32 358.44 Tm (2)Tj /F11 1 Tf 11.9552 0 0 11.9552 390 360.24 Tm 0.1706 Tc (,H)Tj /F9 1 Tf 7.9701 0 0 7.9701 405.96 365.16 Tm 0 Tc (+)Tj -0.1205 -0.9937 TD (2)Tj /F11 1 Tf 11.9552 0 0 11.9552 412.92 360.24 Tm 0.1706 Tc (,H)Tj /F9 1 Tf 7.9701 0 0 7.9701 427.92 358.44 Tm 0 Tc (3)Tj /F3 1 Tf 11.9552 0 0 11.9552 432.6 360.24 Tm 0.7428 Tc [(.T)747.2(h)743.8(e)746.2(r)741.4(e)]TJ /F11 1 Tf 3.9547 0 TD 0 Tc (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 486.48 358.44 Tm (2)Tj /F3 1 Tf 11.9552 0 0 11.9552 496.32 360.24 Tm 0.0001 Tc [(is)-437(the)]TJ -35.4926 -1.2145 TD -0.0002 Tc [(only)-387.6(red)-390.7(v)34(ertex)-397.6(w)4.2(ith)-390.7(f)-2.3(our)-383(r)-1.6(ed)-390.7(neigh)30.9(b)-29.3(ours)-397.1(inducing)-394.5(a)-394.5(p)0.8(ath)]TJ /F11 1 Tf 25.3744 0 TD 0 Tc (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 381.96 343.92 Tm (3)Tj /F11 1 Tf 11.9552 0 0 11.9552 386.76 345.72 Tm (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 393.36 343.92 Tm (0)Tj /F11 1 Tf 11.9552 0 0 11.9552 398.16 345.72 Tm (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 404.76 343.92 Tm (1)Tj /F11 1 Tf 11.9552 0 0 11.9552 409.56 345.72 Tm (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 415.32 343.92 Tm (2)Tj /F3 1 Tf 11.9552 0 0 11.9552 420 345.72 Tm -0.0029 Tc [(.)-615.2(H)-1.6(ence,)]TJ /F11 1 Tf 4.1354 0 TD 0 Tc (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 476.04 343.92 Tm (2)Tj /F3 1 Tf 11.9552 0 0 11.9552 485.52 345.72 Tm -0.0016 Tc [(is)-388.5(xed.)]TJ -34.5892 -1.2045 TD 0.0001 Tc [(F)77(u)1.1(rthermore,)-351.2(t)-1.3(he)-337.8(path)]TJ /F11 1 Tf 9.957 0 TD 0 Tc (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 197.64 329.52 Tm (3)Tj /F11 1 Tf 11.9552 0 0 11.9552 202.44 331.32 Tm (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 209.04 329.52 Tm (0)Tj /F11 1 Tf 11.9552 0 0 11.9552 213.84 331.32 Tm (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 220.44 329.52 Tm (1)Tj /F11 1 Tf 11.9552 0 0 11.9552 225.24 331.32 Tm (y)Tj /F9 1 Tf 7.9701 0 0 7.9701 231 329.52 Tm (2)Tj /F3 1 Tf 11.9552 0 0 11.9552 239.76 331.32 Tm -0.0016 Tc [(cannot)-344.3(b)-30.7(e)-339.5(r)-3(ev)32.6(ersed,)-373(since)]TJ /F11 1 Tf 11.0812 0 TD 0 Tc (x)Tj /F9 1 Tf 7.9701 0 0 7.9701 378.84 329.52 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[(that)-282.9(ha)26.9(v)33.8(e)-288.1(exactly)-297.4(o)-3.2(ne)-278.1(neigh)30.7(b)-29.5(our)-292.9(o)-3.2(utside)]TJ /F11 1 Tf 17.2241 0 TD 0 Tc (H)Tj /F3 1 Tf 0.8933 0 TD 0.4115 Tc [(.T)415.9(h)412.5(e)414.9(s)416.1(e)]TJ -34.7493 -1.2045 TD -0.0003 Tc [(neigh)30.8(b)-29.4(ours)-246.7(are)-247.8(a)-3.1(lready)-237.1(xed)-260.3(b)30.8(y)]TJ /F11 1 Tf 13.3497 0 TD 0 Tc (c)Tj /F3 1 Tf 0.4216 0 TD -0.0015 Tc [(,)-262.5(a)-4.3(nd)-241.4(w)33(e)-249(co)-4.3(lo)-4.3(ur)-243.8(them)-250.5(white.)-423.1(Next,)-272.5(w)33(e)-249(c)1.9(o)-4.3(n)-0.5(sider)-263.9(a)-4.3(ll)-242.4(v)32.7(e)1.9(rtices)]TJ /F11 1 Tf -13.7712 -1.2145 TD 0 Tc (v)Tj /F2 1 Tf 0.793 0 TD ()Tj /F11 1 Tf 0.9435 0 TD (V)Tj /F3 1 Tf 0.793 0 TD (\()Tj /F11 1 Tf 0.3814 0 TD (H)Tj /F3 1 Tf 0.8933 0 TD -0.0013 Tc [(\))-323.9(t)-2.7(ha)-4.1(t)-334(h)-0.3(a)26(v)32.9(e)-339.2(e)2.1(xa)-4.1(ctly)-338.5(t)27.4(w)33.2(o)-345.4(n)-0.3(eig)-4.1(h)29.8(b)-30.4(o)-4.1(urs)]TJ /F11 1 Tf 15.2768 0 TD 0 Tc (u)Tj /F9 1 Tf 7.9701 0 0 7.9701 306.84 568.32 Tm (1)Tj /F11 1 Tf 11.9552 0 0 11.9552 311.52 570.12 Tm 0.1706 Tc (,u)Tj /F9 1 Tf 7.9701 0 0 7.9701 323.52 568.32 Tm 0 Tc (2)Tj /F11 1 Tf 11.9552 0 0 11.9552 332.88 570.12 Tm (/)Tj /F2 1 Tf -0.1104 0 TD ()Tj /F11 1 Tf 0.9435 0 TD (V)Tj /F3 1 Tf 0.7929 0 TD (\()Tj /F11 1 Tf 0.3814 0 TD (H)Tj /F3 1 Tf 0.8933 0 TD 0.0008 Tc [(\).)-430.8(It)-331.9(follo)28.1(w)5.2(s)-335.9(that)]TJ /F11 1 Tf 7.4879 0 TD 0 Tc (u)Tj /F9 1 Tf 7.9701 0 0 7.9701 463.8 568.32 Tm (1)Tj /F11 1 Tf 11.9552 0 0 11.9552 468.48 570.12 Tm (u)Tj /F9 1 Tf 7.9701 0 0 7.9701 475.2 568.32 Tm (2)Tj /F2 1 Tf 11.9552 0 0 11.9552 483.24 570.12 Tm ()Tj /F11 1 Tf 0.9536 0 TD (E)Tj /F3 1 Tf 0.7829 0 TD (\()Tj /F11 1 Tf 0.3814 0 TD (G)Tj /F3 1 Tf 0.7729 0 TD 0.0014 Tc (\),)Tj -37.2893 -1.2045 TD -0.0032 Tc [(b)-32.3(eca)-6(use)]TJ /F11 1 Tf 3.5532 0 TD 0 Tc (G)Tj /F3 1 Tf 1.0338 0 TD -0.0014 Tc [(is)-257.8(cla)25.9(w)3(-)-6.6(f)-3.5(ree,)-292.5(while)]TJ /F11 1 Tf 7.7087 0 TD 0 Tc (v)Tj /F3 1 Tf 0.7628 0 TD 0.0003 Tc [(has)-266.1(a)-514.4(neigh)31.4(b)-28.8(our)-272.1(i)0.3(n)]TJ /F11 1 Tf 8.2708 0 TD 0 Tc (H)Tj /F2 1 Tf 0.9736 0 TD ()Tj /F11 1 Tf 0.8532 0 TD 0.0461 Tc (H)Tj /F3 1 Tf 1.4554 0 TD 0.4216 Tc [(.I)423.3(f)]TJ /F11 1 Tf 1.606 0 TD 0 Tc (u)Tj /F9 1 Tf 7.9701 0 0 7.9701 392.16 553.92 Tm (1)Tj /F3 1 Tf 11.9552 0 0 11.9552 399.96 555.72 Tm 0.0028 Tc (or)Tj /F11 1 Tf 1.1342 0 TD 0 Tc (u)Tj /F9 1 Tf 7.9701 0 0 7.9701 420.24 553.92 Tm (2)Tj /F3 1 Tf 11.9552 0 0 11.9552 427.92 555.72 Tm 0.0008 Tc [(is)-265.6(alre)4.2(ady)-256.1(c)4.2(oloure)4.2(d,)]TJ -29.7712 -1.2045 TD -0.0003 Tc [(then)-280.4(b)-29.4(o)-3.1(th)-280.4(of)-273.4(thes)4.3(e)-288(t)28.4(w)34.2(o)-294.2(v)33.9(e)3.1(rtices)-286.8(are)-278()0.7(x)3.8(e)3.1(d.)-431.9(W)82.3(e)-278(colour)-282.8(the)-278(p)-29.4(os)4.3(s)4.3(i)-0.3(bly)-297.3(uncoloured)-280.4(v)33.9(ertex)-297.3(w)4.1(hite.)]TJ 0 -1.2145 TD -0.002 Tc [(O)-3.8(t)-3.4(herwise,)-363.4(w)32.5(e)-360(co)-4.8(lo)-4.8(ur)]TJ /F11 1 Tf 9.3347 0 TD 0 Tc (u)Tj /F9 1 Tf 7.9701 0 0 7.9701 190.32 525 Tm (1)Tj /F11 1 Tf 11.9552 0 0 11.9552 195 526.8 Tm 0.1706 Tc (,u)Tj /F9 1 Tf 7.9701 0 0 7.9701 207 525 Tm 0 Tc (2)Tj /F3 1 Tf 11.9552 0 0 11.9552 215.76 526.8 Tm 0.0013 Tc [(w)5.7(i)1.3(th)-349(t)30(w)35.8(o)-352.8(d)2.3(ie)4.7(r)-0.1(e)4.7(n)32.4(t)-351.4(c)4.7(olours)5.9(.)-490.5(N)2.6(ote)-336.6(t)-0.1(hat)-341.4(e)4.7(v)35.5(e)4.7(ry)-366(v)35.5(e)4.7(rte)4.7(x)-356(w)35.8(e)-346.6(c)4.7(olour)]TJ -12.0249 -1.2045 TD -0.0001 Tc [(is)-326.8(either)-332.8(white)-338(o)-2.9(r)-322.7(h)0.9(as)-326.8(a)-334.2(w)4.3(hite)-327.9(neigh)31(b)-29.2(our.)]TJ 1.4655 -1.2145 TD -0.0004 Tc [(Finally)84(,)-281.5(l)-0.4(et)-252.8(a)-254.2(v)33.8(ertex)]TJ /F11 1 Tf 8.4514 0 TD 0 Tc (v)Tj /F2 1 Tf 0.7829 0 TD ()Tj /F11 1 Tf 0.9435 0 TD (V)Tj /F3 1 Tf 0.793 0 TD (\()Tj /F11 1 Tf 0.3814 0 TD (H)Tj /F3 1 Tf 0.8933 0 TD -0.0003 Tc [(\))-252.7(h)0.7(a)27(v)33.9(e)-257.9(t)-1.7(hree)-257.9(neigh)30.8(b)-29.4(ours)]TJ /F11 1 Tf 10.1277 0 TD 0 Tc (u)Tj /F9 1 Tf 7.9701 0 0 7.9701 363.72 496.08 Tm (1)Tj /F11 1 Tf 11.9552 0 0 11.9552 368.4 497.88 Tm 0.1706 Tc (,u)Tj /F9 1 Tf 7.9701 0 0 7.9701 380.4 496.08 Tm 0 Tc (2)Tj /F11 1 Tf 11.9552 0 0 11.9552 385.08 497.88 Tm 0.1706 Tc (,u)Tj /F9 1 Tf 7.9701 0 0 7.9701 397.08 496.08 Tm 0 Tc (3)Tj /F3 1 Tf 11.9552 0 0 11.9552 404.76 497.88 Tm -0.0004 Tc (outside)Tj /F11 1 Tf 3.3023 0 TD 0 Tc (H)Tj /F3 1 Tf 0.8933 0 TD -0.0018 Tc [(.)-413.3(T)2.6(hey)-268.7(i)-1.8(nduce)]TJ -32.0296 -1.2045 TD 0.0011 Tc [(a)-343(triangle)]TJ /F11 1 Tf 4.4365 0 TD 0 Tc (K)Tj /F9 1 Tf 7.9701 0 0 7.9701 135 481.68 Tm (3)Tj /F3 1 Tf 11.9552 0 0 11.9552 139.8 483.48 Tm -0.0032 Tc [(,)-354.5(b)-32.3(eca)-6(use)]TJ /F11 1 Tf 4.2558 0 TD 0 Tc (G)Tj /F3 1 Tf 1.1242 0 TD -0.0016 Tc [(is)-338.3(cla)25.7(w)2.8(-)-6.8(f)-3.7(ree.)-503.5(A)29.8(t)-354.3(lea)-4.4(s)3(t)-354.3(t)27.1(w)32.9(o)-355.7(o)-4.4(f)-686.3(them)-350.9(a)-4.4(r)-3(e)-339.5(o)-4.4(f)-345(d)-0.6(eg)-4.4(ree)-349.5(4)-4.4(,)-352.9(a)-4.4(nd)-341.9(no)-345.7(t)27.1(w)32.9(o)]TJ -11.0512 -1.2045 TD -0.0005 Tc [(of)-434.2(them)-440.2(ha)26.8(v)33.7(e)-438.8(a)-434.9(c)2.9(ommon)-441.2(n)0.5(eigh)30.6(b)-29.6(o)-3.3(ur)-443.6(outside)-438.8(t)-1.9(he)-438.8(clique)]TJ /F11 1 Tf 23.9993 0 TD 0 Tc (K)Tj /F9 1 Tf 7.9701 0 0 7.9701 368.88 467.28 Tm (4)Tj /F3 1 Tf 11.9552 0 0 11.9552 379.2 469.08 Tm (=)Tj /F11 1 Tf 1.2145 0 TD (G)Tj /F3 1 Tf 0.7729 0 TD ([)Tj /F2 1 Tf 0.271 0 TD ({)Tj /F11 1 Tf 0.5019 0 TD 0.0389 Tc [(v,)-131.7(u)]TJ /F9 1 Tf 7.9701 0 0 7.9701 430.32 467.28 Tm 0 Tc (1)Tj /F11 1 Tf 11.9552 0 0 11.9552 434.88 469.08 Tm 0.1706 Tc (,u)Tj /F9 1 Tf 7.9701 0 0 7.9701 446.88 467.28 Tm 0 Tc (2)Tj /F11 1 Tf 11.9552 0 0 11.9552 451.56 469.08 Tm 0.1706 Tc (,u)Tj /F9 1 Tf 7.9701 0 0 7.9701 463.56 467.28 Tm 0 Tc (3)Tj /F2 1 Tf 11.9552 0 0 11.9552 468.24 469.08 Tm (})Tj /F3 1 Tf 0.5019 0 TD -0.0023 Tc [(],)-464(b)-31.4(eca)-5.1(use)]TJ /F11 1 Tf -33.6457 -1.2145 TD 0 Tc (m)Tj /F3 1 Tf 0.8532 0 TD (\()Tj /F11 1 Tf 0.3814 0 TD (G)Tj /F3 1 Tf 0.7729 0 TD (\))Tj /F11 1 Tf 0.6725 0 TD (>)Tj /F3 1 Tf 1.0439 0 TD -0.0006 Tc [(2.)-452.3(If)-334(three)-338.5(o)-3.4(f)-334(t)-2(he)-328.4(v)33.6(e)2.8(rtices)]TJ /F11 1 Tf 11.0712 0 TD 0 Tc (u)Tj /F9 1 Tf 7.9701 0 0 7.9701 255.6 452.76 Tm (1)Tj /F11 1 Tf 11.9552 0 0 11.9552 260.28 454.56 Tm 0.1706 Tc (,u)Tj /F9 1 Tf 7.9701 0 0 7.9701 272.28 452.76 Tm 0 Tc (2)Tj /F11 1 Tf 11.9552 0 0 11.9552 276.84 454.56 Tm 0.1706 Tc (,u)Tj /F9 1 Tf 7.9701 0 0 7.9701 288.84 452.76 Tm 0 Tc (3)Tj /F3 1 Tf 11.9552 0 0 11.9552 297.48 454.56 Tm -0.0005 Tc [(are)-328.3(a)-3.3(lready)-337.7(coloured,)-341.8(t)-1.9(hen)-340.8(a)-3.3(ll)-331.7(three)-338.4(a)-3.3(re)-328.3(xed)]TJ -18.8605 -1.2045 TD -0.0311 Tc (by)Tj /F11 1 Tf 1.4454 0 TD 0 Tc (c)Tj /F3 1 Tf 0.8331 0 TD 0.0001 Tc [(and)-410.5(w)34.6(e)-418.1(h)1.1(a)27.4(v)34.3(e)-418.1(n)1.1(othing)-414.3(to)-414.3(do.)-692.5(I)1.8(f)-413.6(t)28.8(w)34.6(o)-414.3(of)-413.6(the)-408(v)34.3(ertices)]TJ /F11 1 Tf 22.3933 0 TD 0 Tc (u)Tj /F9 1 Tf 7.9701 0 0 7.9701 373.68 438.36 Tm (1)Tj /F11 1 Tf 11.9552 0 0 11.9552 378.36 440.16 Tm 0.1706 Tc (,u)Tj /F9 1 Tf 7.9701 0 0 7.9701 390.36 438.36 Tm 0 Tc (2)Tj /F11 1 Tf 11.9552 0 0 11.9552 395.04 440.16 Tm 0.1706 Tc (,u)Tj /F9 1 Tf 7.9701 0 0 7.9701 407.04 438.36 Tm 0 Tc (3)Tj /F3 1 Tf 11.9552 0 0 11.9552 416.64 440.16 Tm -0.0013 Tc [(a)-4.1(r)-2.7(e)-409.4(a)-4.1(lrea)-4.1(dy)-408.7(co)-4.1(lo)-4.1(ured,)]TJ -28.8277 -1.2045 TD 0.0006 Tc [(the)4(n)-359.8(again)-339.7(a)-2.2(ll)-350.7(thre)4(e)-357.4(o)-2.2(f)-342.8(t)-0.8(he)4(m)-358.8(a)-2.2(re)-347.3(x)4.7(e)4(d)1.6(.)-521.4(T)5(he)-357.4(only)-346.6(unc)4(oloure)4(d)-359.8(v)34.8(e)4(rte)4(x)-366.7(g)-2.2(e)4(t)-0.8(s)-346.1(c)4(olour)-352.1(w)5(hite)4(.)-521.4(I)2.3(f)]TJ 0 -1.2145 TD -0.0003 Tc [(only)-307.4(one)-298(o)-3.1(f)-303.5(t)-1.7(hem)-309.5(i)-0.3(s)-306.9(a)-3.1(lready)-297.3(coloured,)-321.5(t)-1.7(hen)-310.5(i)]TJ 18.5089 0 TD -0.0009 Tc [(t)-303.4(i)-0.9(s)-307.5()0.1(xed)-311.1(a)-3.7(nd)-301(w)33.6(e)-318.7(colour)-303.4(the)-298.6(t)27.8(w)33.6(o)-314.9(other)-313.5(v)33.3(ertices)]TJ -18.5089 -1.2045 TD -0.0007 Tc [(white)-288.4(a)-3.5(nd)-280.8(red.)-432.3(Supp)-29.8(ose)-288.4(n)0.3(o)26.6(w)-287.4(that)-283.2(all)-281.8(t)-2.1(hree)-278.4(v)33.5(e)2.7(rtices)]TJ /F11 1 Tf 21.6706 0 TD 0 Tc (u)Tj /F9 1 Tf 7.9701 0 0 7.9701 337.8 395.04 Tm (1)Tj /F11 1 Tf 11.9552 0 0 11.9552 342.48 396.84 Tm 0.1706 Tc (,u)Tj /F9 1 Tf 7.9701 0 0 7.9701 354.48 395.04 Tm 0 Tc (2)Tj /F11 1 Tf 11.9552 0 0 11.9552 359.04 396.84 Tm 0.1706 Tc (,u)Tj /F9 1 Tf 7.9701 0 0 7.9701 371.04 395.04 Tm 0 Tc (3)Tj /F3 1 Tf 11.9552 0 0 11.9552 379.08 396.84 Tm 0.0006 Tc [(are)-277.1(s)5.2(till)-290.5(unc)4(oloure)4(d.)-431(Obs)5.2(e)4(rv)34.8(e)]TJ -25.686 -1.2145 TD 0.0001 Tc [(that)-362.7(they)-377.2(do)-364.1(not)-362.7(h)1.1(a)27.4(v)34.3(e)-377.9(n)1.1(eigh)31.2(b)-29(o)-2.7(urs)-376.7(i)0.1(n)]TJ /F11 1 Tf 16.0598 0 TD 0 Tc (H)Tj /F3 1 Tf 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