49 research outputs found

    Strong chromatic index of subcubic planar multigraphs

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    The strong chromatic index of a multigraph is the minimum k such that the edge set can be k-colored requiring that each color class induces a matching. We verify a conjecture of Faudree, Gyarfas, Schelp and Tuza, showing that every planar multigraph with maximum degree at most 3 has strong chromatic index at most 9, which is sharp. (C) 2015 Elsevier Ltd. All rights reserved

    Strong edge colorings of graphs and the covers of Kneser graphs

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    A proper edge coloring of a graph is strong if it creates no bichromatic path of length three. It is well known that for a strong edge coloring of a kk-regular graph at least 2k12k-1 colors are needed. We show that a kk-regular graph admits a strong edge coloring with 2k12k-1 colors if and only if it covers the Kneser graph K(2k1,k1)K(2k-1,k-1). In particular, a cubic graph is strongly 55-edge-colorable whenever it covers the Petersen graph. One of the implications of this result is that a conjecture about strong edge colorings of subcubic graphs proposed by Faudree et al. [Ars Combin. 29 B (1990), 205--211] is false

    Coloring, List Coloring, and Painting Squares of Graphs (and other related problems)

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    We survey work on coloring, list coloring, and painting squares of graphs; in particular, we consider strong edge-coloring. We focus primarily on planar graphs and other sparse classes of graphs.Comment: 32 pages, 13 figures and tables, plus 195-entry bibliography, comments are welcome, published as a Dynamic Survey in Electronic Journal of Combinatoric
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