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^*

^*この研究の対応する著者

教育学部

研究成果: Article › 査読

6 被引用数 (Scopus)

抄録

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.

本文言語	English
ページ（範囲）	1002-1010
ページ数	9
ジャーナル	Topology and its Applications
巻	157
号	6
DOI	https://doi.org/10.1016/j.topol.2009.12.016
出版ステータス	Published - 2010 4月 15

ASJC Scopus subject areas

幾何学とトポロジー

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10.1016/j.topol.2009.12.016

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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 - Link

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KW - Planar graph

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

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