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

Toshiki Endo, Tomoko Itoh, Kouki Taniyama

Research output: Contribution to journalArticle

3 Citations (Scopus)

### 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.

Original language English 1002-1010 9 Topology and its Applications 157 6 https://doi.org/10.1016/j.topol.2009.12.016 Published - 2010 Apr 15

### Fingerprint

Partial Order
Knot
Diagram
Prime knot
Alternating knot
Crossing number
Partial ordering
Less than or equal to
Graph in graph theory
Smoothing

### Keywords

• Graph minor
• Knot
• Partial order
• Planar graph

### ASJC Scopus subject areas

• Geometry and Topology

### Cite this

A graph-theoretic approach to a partial order of knots and links. / Endo, Toshiki; Itoh, Tomoko; Taniyama, Kouki.

In: Topology and its Applications, Vol. 157, No. 6, 15.04.2010, p. 1002-1010.

Research output: Contribution to journalArticle

Endo, Toshiki ; Itoh, Tomoko ; Taniyama, Kouki. / A graph-theoretic approach to a partial order of knots and links. In: Topology and its Applications. 2010 ; Vol. 157, No. 6. pp. 1002-1010.
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