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

Toshiki Endo; Tomoko Itoh; Kouki Taniyama

doi:10.1016/j.topol.2009.12.016

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

Toshiki Endo, Tomoko Itoh, Kouki Taniyama^*

^*Corresponding author for this work

School of Education

Research output: Contribution to journal › Article › peer-review

6 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
Pages (from-to)	1002-1010
Number of pages	9
Journal	Topology and its Applications
Volume	157
Issue number	6
DOIs	https://doi.org/10.1016/j.topol.2009.12.016
Publication status	Published - 2010 Apr 15

Keywords

Graph minor
Knot
Link
Partial order
Planar graph

ASJC Scopus subject areas

Geometry and Topology

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10.1016/j.topol.2009.12.016

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AU - Itoh, Tomoko

AU - Taniyama, Kouki

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N2 - 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.

AB - 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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KW - Knot

KW - Link

KW - Partial order

KW - Planar graph

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

Abstract

Keywords

ASJC Scopus subject areas

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