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  • A note on domination and independence-domination numbers of graphs
    Milanič, Martin, 1980-
    Vizing's conjecture is true for graphs ▫$G$▫ satisfying ▫$\gamma^i(G) = \gamma(G)$▫, where ▫$\gamma(G)$▫ is the domination number of a graph ▫$G$▫ and ▫$\gamma^i(G)$▫ is the independence-domination ... number of ▫$G$▫, that is, the maximum, over all independent sets ▫$I$▫ in ▫$G$▫, of the minimum number of vertices needed to dominate ▫$I$▫. The equality ▫$\gamma^i(G) = \gamma(G)$▫ is known to hold for all chordal graphs and for chordless cycles of length ▫$0 \pmod{3}$▫. We prove some results related to graphs for which the above equality holds. More specifically, we show that the problems of determining whether ▫$\gamma^i(G) = \gamma(G) = 2$▫ and of verifying whether ▫$\gamma^i(G) \ge 2$▫ are NP-complete, even if ▫$G$▫ is weakly chordal. We also initiate the study of the equality ▫$\gamma^i = \gamma$▫ in the context of hereditary graph classes and exhibit two infinite families of graphs for which ▫$\gamma^i < \gamma$▫.
    Vir: Ars mathematica contemporanea : special issue Bled'11 (Vol. 6, no. 1, 2013, str. 89-97)
    Vrsta gradiva - prispevek na konferenci ; neleposlovje za odrasle
    Leto - 2013
    Jezik - angleški
    COBISS.SI-ID - 1024423764

    Povezava(-e):

    http://amc.imfm.si/index.php/amc/article/view/282
    Digitalna knjižnica Slovenije - dLib.si
    Repozitorij Univerze na Primorskem - RUP

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