含有3-圈的平面图的有效染色数
The Valid Coloring Number of Plane Graphs Containing3-Cycles
DOI: 10.12677/AAM.2025.141005, PDF,   
作者: 沈儒雄：浙江师范大学数学科学学院，浙江 金华
关键词: 平面图；彩虹面；有效染色；Plane Graph； Rainbow Face； Valid Coloring
摘要: 给定平面图G的一个顶点染色，如果图G的某个面F 的所有顶点颜色各不相同，我们称面F 为彩 虹面。 而如果平面图G中没有任何一个面是彩虹面，我们称这种染色为有效染色. 在这种有效 染色方案中，所使用的颜色种类的最大值定义为该平面图的有效染色数，记作χf (G)。 Jungiˇc, Kr´al／和Sˇkrekovski研究了一类围长至少为4的平面图的有效染色数。 本文主要研究了一类既包 含3-圈又包含长度至少为5的面圈的平面图的有效染色数井得到了它的下界。
Abstract: Given a vertex coloring of a plane graph G, if all the vertices of a face F of G receive mutually different colors, then the face F is called a rainbow face. A valid coloring is a coloring of G such that no face of G is rainbow. The maximum number of colors used in a valid coloring of a plane graph G is referred to as the valid coloring number, denoted by χf (G). Jungiˇc, Kr´al／ and Sˇkrekovski focused on the valid coloring number of a class of plane graphs with girth at least 4. In this paper, we mainly study the valid coloring number of a class of plane graphs containing 3-cycles and faces with cycles of length at least 5 and get its lower bound.
文章引用：沈儒雄. 含有3-圈的平面图的有效染色数[J]. 应用数学进展, 2025, 14(1): 24-32. https://doi.org/10.12677/AAM.2025.141005

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