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 languageEnglish
    Pages (from-to)1002-1010
    Number of pages9
    JournalTopology and its Applications
    Volume157
    Issue number6
    DOIs
    Publication statusPublished - 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
    • Link
    • 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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