Geodesic
Intrinsic knotting and linking of complete graphs
Flapan, Erica1
1Department of Mathematics, Pomona College, Claremont, CA 91711, USA
Algebraic and Geometric Topology, Tome 2 (2002) no. 1, pp. 371-380
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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.

DOI : 10.2140/agt.2002.2.371
Keywords: embedded graphs, intrinsic knotting, intrinsic linking

Flapan, Erica  1

1 Department of Mathematics, Pomona College, Claremont, CA 91711, USA 
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Flapan, Erica. Intrinsic knotting and linking of complete graphs. Algebraic and Geometric Topology, Tome 2 (2002) no. 1, pp. 371-380. doi: 10.2140/agt.2002.2.371

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