最大度至少为9的平面图的弱邻点可区别边色数

摘要

介绍了一种新的邻点可区别边染色：弱邻点可区别边染色。图G的弱邻点可区别边染色是G的一个正常边染色，使得任何一个相邻的最大度点有不同的颜色集合。对于图G的一个弱邻点可区别边染色所需要的最小颜色数，记作字′a△（G）。该文证明了：若G是最大度至少为9的平面图，则字′a△（G）≤△+2。%This paper introduces a type of adjacent vertex distinguishing edge-coloring,weak adjacent vertex distinguish- ing edge-oloring. The weak adjacent vertex distinguishing edge-coloring of graph G is a proper edge-coloring of G such that any pair of adjacent △-vertices u and v see distinct sets of colors. The minimum number of colors required for a weak adjacent vertex distinguishing edge-coloring of G is denoted by x′a△(G). We prove that if G is a planar graph with △≥9, then x′a△(G)≤△+2.