A remark on star-C4 and wheel-C4 Ramsey numbers

Yanbo Zhang, Haitze J. Broersma, Yaojun Chen

    Research output: Contribution to journalArticleAcademicpeer-review

    Abstract

    Given two graphs G1 and G2, the Ramsey number R(G1;G2) is the smallest integer N such that, for any graph G of order N, either G1 is a subgraph of G, or G2 is a subgraph of the complement of G. Let Cn denote a cycle of order n, Wn a wheel of order n+1 and Sn a star of order n. In this paper, it is shown that R(Wn;C4) = R(Sn+1;C4) for n ≥ 6. Based on this result and Parsons' results on R(Sn+1;C4), we establish the best possible general upper bound for R(Wn;C4) and determine some exact values for R(Wn;C4).
    Original languageUndefined
    Pages (from-to)110-114
    Number of pages5
    JournalElectronic journal of graph theory and applications
    Volume2
    Issue number2
    DOIs
    Publication statusPublished - 2014

    Keywords

    • EWI-25792
    • MSC-04C
    • Quadrilateral
    • Ramsey number
    • IR-94683
    • 4-Cycle
    • Wheel
    • METIS-309924
    • Star

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