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  • On the b-chromatic number of regular graphs
    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 ▫$d+1$▫, the ▫$b$▫-chromatic number of an arbitrary ▫$d$▫-regular graph with girth ▫$g=5$▫ is at least ▫$\lfloor \frac{d+1}{2} \rfloor$▫ and every $d$-regular graph, ▫$d \ge 6$▫, with diameter at least ▫$d$▫ and with no ▫$4$▫-cycles has b-chromatic numer ▫$d+1$▫.
    Vir: Discrete applied mathematics. - ISSN 0166-218X (Vol. 159, iss. 13, 2011, str. 1303-1310)
    Vrsta gradiva - članek, sestavni del
    Leto - 2011
    Jezik - angleški
    COBISS.SI-ID - 15914329

vir: Discrete applied mathematics. - ISSN 0166-218X (Vol. 159, iss. 13, 2011, str. 1303-1310)
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