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 Kn 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 Kr in R3 contains a knot Q with |a2(Q)| > m-1, where a2(Q) denotes the second coefficient of the Conway polynomial of Q.
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