#### 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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