Intrinsic knotting and linking of complete graphs
Geometric Topology
2014-10-01 v1
Abstract
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.
Keywords
Cite
@article{arxiv.math/0205231,
title = {Intrinsic knotting and linking of complete graphs},
author = {Erica Flapan},
journal= {arXiv preprint arXiv:math/0205231},
year = {2014}
}
Comments
Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol2/agt-2-17.abs.html