On star-critical and upper size Ramsey numbers

Yanbo Zhang, Haitze J. Broersma, Yaojun Chen

    Research output: Contribution to journalArticleAcademicpeer-review

    9 Citations (Scopus)

    Abstract

    In this paper, we study the upper size Ramsey number u(G1,G2)u(G1,G2), defined by Erdős and Faudree, as well as the star-critical Ramsey number r∗(G1,G2)r∗(G1,G2), defined by Hook and Isaak. We define Ramsey-full graphs and size Ramsey good graphs, and perform a detailed study on these graphs. We generalize earlier results by determining u(nKk,mKl)u(nKk,mKl) and r∗(nKk,mKl)r∗(nKk,mKl) for k,l≥3k,l≥3 and large m,nm,n; u(Cn,Cm)u(Cn,Cm) for mm odd, with n>m≥3n>m≥3; and r∗(Cn,Cm)r∗(Cn,Cm) for mm odd, with n≥m≥3n≥m≥3 and (m,n)≠(3,3)(m,n)≠(3,3).
    Original languageEnglish
    Pages (from-to)174-180
    Number of pages7
    JournalDiscrete applied mathematics
    Volume202
    DOIs
    Publication statusPublished - 31 Mar 2016

    Keywords

    • EWI-26837
    • MSC-05C
    • Upper size Ramsey number
    • IR-99581
    • Ramsey-full graph
    • Star-critical Ramsey number
    • METIS-316047
    • Size Ramsey good graph

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