不含4-圈的IC-平面图的严格邻点可区别边染色

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不含4-圈的IC-平面图的严格邻点可区别边染色
Strict Neighbor-Distinguishing Edge-Coloring of IC-Planar Graphs without 4-Cycles

DOI: 10.12677/AAM.2025.144141, PDF,
作者: 王加炎：浙江师范大学数学科学学院，浙江金华
关键词: 严格邻点可区别边染色；IC-平面图；圈；Strict Neighbor-Distinguishing Edge-Coloring； IC-Planar Graph； Cycle

摘要: 图的严格邻点可区别边染色是指图中的任意一对相邻顶点的颜色集合互相不包含。称使得图具有严格邻点可区别边染色的最小正整数为图的严格邻点可区别边色数。本文运用权转移方法证明：对于不含4-圈的IC-平面图，其严格邻点可区别边色数为两倍最大度与13 的和。

Abstract: The strict neighbor-distinguishing edge coloring of a graph refers to an edge coloring where for any pair of adjacent vertices, their respective color sets neither contain nor are contained within each other. The smallest positive integer that enables a graph to admit such a coloring is called the strict neighbor-distinguishing edge chromatic number. In this paper, we employ the discharging method to prove that for IC-planar graphs without 4-cycles, the strictly adjacent vertex-distinguishing edge chromatic number equals the sum of twice the maximum degree and 13.

文章引用：王加炎. 不含4-圈的IC-平面图的严格邻点可区别边染色[J]. 应用数学进展, 2025, 14(4): 75-82. https://doi.org/10.12677/AAM.2025.144141

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