On intrinsically knotted or completely 3-linked graphs

Ryo Hanaki, Ryo Nikkuni, Kouki Taniyama, Akiko Yamazaki

    Research output: Contribution to journalArticle

    12 Citations (Scopus)

    Abstract

    We say that a graph is intrinsically knotted or completely 3-linked if every embedding of the graph into the 3-sphere contains a nontrivial knot or a 3-component link each of whose 2-component sublinks is nonsplittable. We show that a graph obtained from the complete graph on seven vertices by a finite sequence of ΔY-exchanges and YΔ-exchanges is a minor-minimal intrinsically knotted or completely 3-linked graph.

    Original languageEnglish
    Pages (from-to)407-425
    Number of pages19
    JournalPacific Journal of Mathematics
    Volume252
    Issue number2
    DOIs
    Publication statusPublished - 2011

    Fingerprint

    Graph in graph theory
    Complete Graph
    Knot
    Minor

    Keywords

    • ΔY-exchange
    • Intrinsic knottedness
    • Spatial graph
    • YΔ-exchange

    ASJC Scopus subject areas

    • Mathematics(all)

    Cite this

    On intrinsically knotted or completely 3-linked graphs. / Hanaki, Ryo; Nikkuni, Ryo; Taniyama, Kouki; Yamazaki, Akiko.

    In: Pacific Journal of Mathematics, Vol. 252, No. 2, 2011, p. 407-425.

    Research output: Contribution to journalArticle

    Hanaki, Ryo ; Nikkuni, Ryo ; Taniyama, Kouki ; Yamazaki, Akiko. / On intrinsically knotted or completely 3-linked graphs. In: Pacific Journal of Mathematics. 2011 ; Vol. 252, No. 2. pp. 407-425.
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