A graph-theoretic approach to a partial order of knots and links

Toshiki Endo, Tomoko Itoh, Kouki Taniyama*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)1002-1010
Number of pages9
JournalTopology and its Applications
Issue number6
Publication statusPublished - 2010 Apr 15


  • Graph minor
  • Knot
  • Link
  • Partial order
  • Planar graph

ASJC Scopus subject areas

  • Geometry and Topology


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