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

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

2008-06-22

arxiv.org/abs/0806.3595v1

Mathematics

Geometric Topology

15 pages, 27 figures

Scientific paper

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.

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