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

2008/06/22 by Toshiki Endo, Endo, Toshiki, Tomoko Itoh +3
Computer Science · Mathematics · #57M25 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #math.GT #msc:57M25 #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.0806.3595

15 pages, 27 figures

arxiv created 2008/06/22 · openalex publication_date 2008/06/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We say that a link L₁ is an s-major of a link L₂ if any diagram of L₁ can be transformed into a diagram of L₂ 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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