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  • Clique coverings and claw-free graphs
    Bujtás, Csilla ...
    Let ▫$\mathscr{C}$▫ be a clique covering for ▫$E(G)$▫ and let ▫$v$▫ be a vertex of ▫$G$▫. The valency of vertex ▫$v$▫ (with respect to ▫$\mathscr{C}$)▫, denoted by ▫$val_{\mathscr{C}}(v)$▫, is the ... number of cliques in ▫$\mathscr{C}$▫ containing ▫$v$▫. The local clique cover number of ▫$G$▫, denoted by ▫$lcc(G)$▫, is defined as the smallest integer ▫$k$▫, for which there exists a clique covering for ▫$E(G)$▫ such that ▫$val_{\mathscr{C}}(v)$▫ is at most ▫$k$▫, for every vertex ▫$v\in V(G)$▫. In this paper, among other results, we prove that if ▫$G$▫ is a claw-free graph, then ▫$lcc(G)+\chi(G)\leq n+1$▫.
    Vir: European journal of combinatorics = Journal européen de combinatoire = Europäische Zeitschrift für Kombinatorik. - ISSN 0195-6698 (Vol. 88, Aug. 2020, art. 103114 (9 str.))
    Vrsta gradiva - članek, sestavni del ; neleposlovje za odrasle
    Leto - 2020
    Jezik - angleški
    COBISS.SI-ID - 24557059

    Povezava(-e):

    https://doi.org/10.1016/j.ejc.2020.103114
    DOI

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