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https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/55467
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| 题名: | Adaptable chromatic number of graph products |
| 作者: | Pavol Hell;Pan, Zhishi;Wong, Tsai-Lien;Zhu, Xuding |
| 贡献者: | 淡江大學數學學系 |
| 关键词: | Chromatic number;Adaptable chromatic number;Categorical product;Cartesian product;Categorical power;Cartesian power |
| 日期: | 2009-11 |
| 上传时间: | 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 |
| 显示于类别: | [應用數學與數據科學學系] 期刊論文
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