A large complete graph in a space contains a link with large link invariant

Minori Shirai, Kouki Taniyama

    Research output: Contribution to journalArticle

    1 Citation (Scopus)

    Abstract

    Let k be a non-negative integer. Then any embedding of the complete graph on 6 · 2k vertices into a three-space contains a two-component link with the absolute value of its linking number greater than or equal to 2k. Let j be a non-negative integer. Then any embedding of the complete graph on 48 · 2k vertices into a three-space contains a knot with the absolute value of the second coefficient of its Conway polynomial greater than or equal to 22j.

    Original languageEnglish
    Pages (from-to)915-919
    Number of pages5
    JournalJournal of Knot Theory and its Ramifications
    Volume12
    Issue number7
    DOIs
    Publication statusPublished - 2003 Nov

    Fingerprint

    Link Invariants
    Absolute value
    Complete Graph
    Non-negative
    Conway Polynomial
    Linking number
    Integer
    Knot
    Coefficient

    Keywords

    • Complete graph
    • Intrinsic knotting
    • Intrinsic linking
    • Linking number
    • Second coefficient of Conway polynomial
    • Spatial graph

    ASJC Scopus subject areas

    • Algebra and Number Theory

    Cite this

    A large complete graph in a space contains a link with large link invariant. / Shirai, Minori; Taniyama, Kouki.

    In: Journal of Knot Theory and its Ramifications, Vol. 12, No. 7, 11.2003, p. 915-919.

    Research output: Contribution to journalArticle

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