Lattice stick number of spatial graphs

Hyungkee Yoo, Chaeryn Lee, Seungsang Oh

    Research output: Contribution to journalArticlepeer-review

    3 Citations (Scopus)

    Abstract

    The lattice stick number of knots is defined to be the minimal number of straight sticks in the cubic lattice required to construct a lattice stick presentation of the knot. We similarly define the lattice stick number sL(G) of spatial graphs G with vertices of degree at most six (necessary for embedding into the cubic lattice), and present an upper bound in terms of the crossing number c(G) sL(G) ≤ 3c(G) + 6e - 4v - 2s + 3b + k, where G has e edges, v vertices, s cut-components, b bouquet cut-components, and k knot components.

    Original languageEnglish
    Article number1850048
    JournalJournal of Knot Theory and its Ramifications
    Volume27
    Issue number8
    DOIs
    Publication statusPublished - 2018 Jul 1

    Bibliographical note

    Funding Information:
    Seungsang Oh was supported by the National Research Foundation of Korea (NRF) Grant funded by the Korea Government (MSIP) (No. NRF-2017R1A2B2007216).

    Publisher Copyright:
    © 2018 World Scientific Publishing Company.

    Keywords

    • Graph
    • lattice stick number
    • upper bound

    ASJC Scopus subject areas

    • Algebra and Number Theory

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