Plane curves in an immersed graph in R2

Marisa Sakamoto, Kouki Taniyama

    Research output: Contribution to journalArticle

    3 Citations (Scopus)

    Abstract

    For any chord diagram on a circle there exists a complete graph on sufficiently many vertices such that any generic immersion of it to the plane contains a plane-closed curve whose chord diagram contains the given chord diagram as a sub-chord diagram. For any generic immersion of the complete graph on six vertices to the plane, the sum of averaged invariants of all Hamiltonian plane curves in it is congruent to one quarter modulo one-half.

    Original languageEnglish
    Article number1350003
    JournalJournal of Knot Theory and its Ramifications
    Volume22
    Issue number2
    DOIs
    Publication statusPublished - 2013 Feb

    Fingerprint

    Chord Diagrams
    Plane Curve
    Graph in graph theory
    Immersion
    Complete Graph
    Closed curve
    Congruent
    Modulo
    Circle
    Invariant

    Keywords

    • chord diagram
    • Immersed graph
    • knot
    • plane curve

    ASJC Scopus subject areas

    • Algebra and Number Theory

    Cite this

    Plane curves in an immersed graph in R2 . / Sakamoto, Marisa; Taniyama, Kouki.

    In: Journal of Knot Theory and its Ramifications, Vol. 22, No. 2, 1350003, 02.2013.

    Research output: Contribution to journalArticle

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