Intrinsic knotting and linking of complete graphs

Details Intrinsic knotting and linking of complete graphs Intrinsic knotting and linking of complete graphs

2002-05-22

arxiv.org/abs/math/0205231v1

Algebr. Geom. Topol. 2 (2002) 371-380

Mathematics

Geometric Topology

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol2/agt-2-17.abs.html

Scientific paper

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.

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