最大度至多为5的平面图的Injective边染色

Injective Edge-Coloring of Planar Graphs with Maximum Degree at Most 5

摘要: 图的injective边染色是指图中的任意两条距离为2的边或在同一个三角形的边不能染相同的颜色。称使得图具有injective边染色的最小正整数为图的injective边色数。本文运用权转移方法证明了以下结论：对于最大度小于等于5且无4-圈的平面图，其injective边色数小于等于21。

Abstract: An injective edge-coloring of a graph is that any two edges at distance two, or are in a triangle cannot be colored with the same color. The smallest integer of colors needed for an injective edge-coloring of a graph is called the injective chromatic index. In this paper, we prove the following conclusion by using the discharging method: For a planar graph with maximum degree at most 5 and without 4-cycles, its injective chromatic index is at most 21.