A note on Ramsey numbers for fans

Yanbo Zhang, Haitze J. Broersma, Yaojun Chen

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    Abstract

    For two given 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 G contains G1 as a subgraph or the complement of G contains G2 as a subgraph. A fan Fl is l triangles sharing exactly one vertex. In this note, it is shown that R(Fn, Fm) = 4n + 1 for n ≥ max{m 2 − m/2, 11m/2 − 4}.
    Original languageUndefined
    Pages (from-to)19-23
    Number of pages5
    JournalBulletin of the Australian Mathematical Society
    Volume92
    Issue number1
    DOIs
    Publication statusPublished - Aug 2015

    Keywords

    • MSC-05C
    • EWI-27035
    • IR-100672
    • Ramsey number
    • METIS-317206
    • Fan

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