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  • On the b-chromatic number of regular graphs [Elektronski vir]
    Cabello, Sergio ; Jakovac, Marko
    The b-chromatic number of a graph ▫$G$▫ is the largest integer ▫$k$▫ such that ▫$G$▫ admits a proper ▫$k$▫-coloring in which every color class contains at least one vertex that has a neighbor in each ... of the other color classes. We prove that every ▫$d$▫-regular graph with at least ▫$2d^3$▫ vertices has ▫$b$▫-chromatic number ▫$d+1$▫, that the ▫$b$▫-chromatic number of an arbitrary ▫$d$▫-regular graph with girth ▫$g=5$▫ is at least ▫$\lfloor \frac{d+1}{2} \rfloor$▫ and that every $d$-regular graph, ▫$d \ge 6$▫, with diameter at least ▫$d$▫ and with no ▫$4$▫-cycles admits a ▫$b$▫-coloring with ▫$d+1$▫ colors.
    Vir: Preprint series [Elektronski vir]. - ISSN 2232-2094 (Vol. 48, št. 1131, 2010, str. 1-11)
    Vrsta gradiva - e-članek
    Leto - 2010
    Jezik - angleški
    COBISS.SI-ID - 15695449

    Povezava(-e):

    http://www.imfm.si/preprinti/PDF/01131.pdf

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