Algebraic and Geometric Topology 2 (2002), paper no. 17, pages 371-380.

Intrinsic knotting and linking of complete graphs

Erica Flapan

Abstract. We show that for every m in N, there exists an n in N such that every embedding of the complete graph K_n in R^3 contains a link of two components whose linking number is at least m. Furthermore, there exists an r in N such that every embedding of K_r in R^3 contains a knot Q with |a_2(Q)| > m-1, where a_2(Q) denotes the second coefficient of the Conway polynomial of Q.

Keywords. Embedded graphs, intrinsic knotting, intrinsic linking

AMS subject classification. Primary: 57M25. Secondary: 05C10.

DOI: 10.2140/agt.2002.2.371

E-print: arXiv:math.GT/0205231

Submitted: 13 March 2002. Accepted: 13 April 2002. Published: 21 May 2002.

Notes on file formats

Erica Flapan
Department of Mathematics, Pomona College
Claremont, CA 91711, U.S.A.
Email: eflapan@pomona.edu

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