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Intrinsic Knotting And Linking Of Complete Graphs, Erica Flapan
Intrinsic Knotting And Linking Of Complete Graphs, Erica Flapan
Pomona Faculty Publications and Research
We show that for every m∈N, there exists an n∈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∈N such that every embedding of Kr in R3 contains a knot Q with |a2(Q)| ≥ m, where a2(Q) denotes the second coefficient of the Conway polynomial of Q.