A Graph-Theoretic Approach to a Partial Order of Knots and Links

Toshiki Endo; Tomoko Itoh; Kouki Taniyama

A Graph-Theoretic Approach to a Partial Order of Knots and Links

Geometric Topology 2008-06-24 v1

Authors: Toshiki Endo , Tomoko Itoh , Kouki Taniyama

Abstract

We say that a link $L_1$ is an s-major of a link $L_2$ if any diagram of $L_1$ can be transformed into a diagram of $L_2$ by changing some crossings and smoothing some crossings. This relation is a partial ordering on the set of all prime alternating links. We determine this partial order for all prime alternating knots and links with the crossing number less than or equal to six. The proofs are given by graph-theoretic methods.

Keywords

knots and links partial order s-major prime alternating links crossing number graph-theoretic methods diagram transformation

Cite

@article{arxiv.0806.3595,
  title  = {A Graph-Theoretic Approach to a Partial Order of Knots and Links},
  author = {Toshiki Endo and Tomoko Itoh and Kouki Taniyama},
  journal= {arXiv preprint arXiv:0806.3595},
  year   = {2008}
}

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15 pages, 27 figures

A Graph-Theoretic Approach to a Partial Order of Knots and Links

Abstract

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