Algebraic & Geometric Topology 2 (2002) 371–380

DOI: 10.2140/agt.2002.2.371

arXiv: math.GT/0205231

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 R³ 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 R³ 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

Primary: 57M25

Secondary: 05C10

References

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Publication

Received: 13 March 2002
Accepted: 28 March 2002
Published: 21 May 2002

Authors