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    題名: Adaptable chromatic number of graph products
    作者: Pavol Hell;Pan, Zhishi;Wong, Tsai-Lien;Zhu, Xuding
    貢獻者: 淡江大學數學學系
    關鍵詞: Chromatic number;Adaptable chromatic number;Categorical product;Cartesian product;Categorical power;Cartesian power
    日期: 2009-11
    上傳時間: 2011-08-22 16:18:41 (UTC+8)
    出版者: Amsterdam: Elsevier BV * North-Holland
    摘要: A colouring of the vertices of a graph (or hypergraph) G is adapted to a given colouring of the edges of G if no edge has the same colour as both (or all) its vertices. The adaptable chromatic number of G is the smallest integer k such that each edge-colouring of G by colours 1,2,…,k admits an adapted vertex-colouring of G by the same colours 1,2,…,k. (The adaptable chromatic number is just one more than a previously investigated notion of chromatic capacity.) The adaptable chromatic number of a graph G is smaller than or equal to the ordinary chromatic number of G. While the ordinary chromatic number of all (categorical) powers Gk of G remains the same as that of G, the adaptable chromatic number of Gk may increase with k. We conjecture that for all sufficiently large k the adaptable chromatic number of Gk equals the chromatic number of G. When G is complete, we prove this conjecture with k≥4, and offer additional evidence suggesting it may hold with k≥2. We also discuss other products and propose several open problems.
    關聯: Discrete Mathematics 309(21), pp.6153-6159
    DOI: 10.1016/j.disc.2009.05.029
    顯示於類別:[數學學系暨研究所] 期刊論文

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