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arXiv:math/0205231 [math.GT]AbstractReferencesReviewsResources

Intrinsic knotting and linking of complete graphs

Erica Flapan

Published 2002-05-22Version 1

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.

Comments: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol2/agt-2-17.abs.html
Journal: Algebr. Geom. Topol. 2 (2002) 371-380
Categories: math.GT
Subjects: 57M25, 05C10
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