Аннотация:
Доказано, что предписанный хроматический класс любого плоского графа
степени 14 или выше равен максимальной степени. Доказательство основано на обобщении теоремы Коцига о минимальном весе ребра в плоском графе.
Библиогр. 14 назв.
Watcharintorn Ruksasakchai, Pongpat Sittitrai, “Sufficient Conditions make Graphs Edge DP-Δ-Colorable”, Graphs and Combinatorics, 41:1 (2025)
Patcharapan Jumnongnit, Kittikorn Nakprasit, Watcharintorn Ruksasakchai, Pongpat Sittitrai, “Edge DP-coloring of planar graphs without 4-cycles and specific cycles”, Discrete Mathematics, 348:4 (2025), 114353
Borodin O.V., “Colorings of Plane Graphs: a Survey”, Discrete Math., 313:4 (2013), 517–539
Clément Charpentier, Mickael Montassier, André Raspaud, “Minmax degree of graphs (Extended abstract)”, Electronic Notes in Discrete Mathematics, 38 (2011), 251
Oleg V. Borodin, Alexandr V. Kostochka, Naeem N. Sheikh, Gexin Yu, “M‐degrees of quadrangle‐free planar graphs”, Journal of Graph Theory, 60:1 (2009), 80
Stephan Dominique Andres, “Lightness of digraphs in surfaces and directed game chromatic number”, Discrete Mathematics, 309:11 (2009), 3564
Oleg V. Borodin, Anna O. Ivanova, Alexandr V. Kostochka, Naeem N. Sheikh, “MINIMAX DEGREES OF QUASIPLANAR GRAPHS WITH NO SHORT CYCLES OTHER THAN TRIANGLES”, Taiwanese J. Math., 12:4 (2008)
O. V. Borodin, A. O. Ivanova, A. V. Kostochka, N. N. Sheikh, “Minimax degrees of quasiplane graphs without 4-faces”, Сиб. электрон. матем. изв., 4 (2007), 435–439
Wei-Fan Wang, “Edge-partitions of graphs of nonnegative characteristic and their game coloring numbers”, Discrete Mathematics, 306:2 (2006), 262
Mohammad Hosseini Dolama, Éric Sopena, Xuding Zhu, “Incidence coloring of k-degenerated graphs”, Discrete Mathematics, 283:1-3 (2004), 121
Wenjie He, Xiaoling Hou, Ko‐Wei Lih, Jiating Shao, Weifan Wang, Xuding Zhu, “Edge‐partitions of planar graphs and their game coloring numbers”, Journal of Graph Theory, 41:4 (2002), 307
Xuding Zhu, “The Game Coloring Number of Planar Graphs”, Journal of Combinatorial Theory, Series B, 75:2 (1999), 245