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  • More results on ▫$r$▫-inflated graphs: arboricity, thickness, chromatic number and fractional chromatic number
    Albertson, Michael O. ; Boutin, Debra L. ; Gethner, Ellen
    The ▫$r$▫-inflation of a graph ▫$G$▫ is the lexicographic product ▫$G$▫ with ▫$K_r$▫. A graph is said to have thickness ▫$t$▫ if its edges can be partitioned into ▫$t$▫ sets, each of which induces a ... planar graph, and ▫$t$▫ is smallest possible. In the setting of the ▫$r$▫-inflation of planar graphs, we investigate the generalization of Ringel's famous Earth-Moon problem: What is the largest chromatic number of any thickness-t graph? In particular, we study classes of planar graphs for which we can determine both the thickness and chromatic number of their 2-inflations, and provide bounds on these parameters for their ▫$r$▫-inflations. Moreover, in the same setting, we investigate arboricity and fractional chromatic number as well. We end with a list of open questions.
    Vir: Ars mathematica contemporanea. - ISSN 1855-3966 (Vol. 4, no. 1, 2011, str. 5-24)
    Vrsta gradiva - članek, sestavni del
    Leto - 2011
    Jezik - angleški
    COBISS.SI-ID - 16260697

    Povezava(-e):

    http://amc.imfm.si/index.php/amc/article/view/175
    Digitalna knjižnica Slovenije - dLib.si

vir: Ars mathematica contemporanea. - ISSN 1855-3966 (Vol. 4, no. 1, 2011, str. 5-24)

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