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Intrinsic knotting and linking of complete graphs

Erica Flapan

Algebraic & Geometric Topology 2 (2002) 371–380

arXiv: math.GT/0205231

Abstract

We show that for every m , there exists an n such that every embedding of the complete graph Kn in 3 contains a link of two components whose linking number is at least m. Furthermore, there exists an r such that every embedding of Kr in 3 contains a knot Q with |a2(Q)| m, where a2(Q) denotes the second coefficient of the Conway polynomial of Q.

Keywords
embedded graphs, intrinsic knotting, intrinsic linking
Mathematical Subject Classification 2000
Primary: 57M25
Secondary: 05C10
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Publication
Received: 13 March 2002
Accepted: 28 March 2002
Published: 21 May 2002
Authors
Erica Flapan
Department of Mathematics
Pomona College
Claremont, CA 91711
USA