Algebraic and Geometric Topology 2 (2002),
paper no. 17, pages 371-380.
Intrinsic knotting and linking of complete graphs
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.
Embedded graphs, intrinsic knotting, intrinsic linking
AMS subject classification.
Submitted: 13 March 2002.
Accepted: 13 April 2002.
Published: 21 May 2002.
Notes on file formats
Department of Mathematics, Pomona College
Claremont, CA 91711, U.S.A.
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