围长至少为4的平面图的邻点可区别边色数(英文)  

Adjacent Vertex Distinguishing Edge-colorings of Planar Graphs with Girth at Least Four

作　　者：严丞超[1] 黄丹君[1] 王维凡[1] 

机构地区：[1]浙江师范大学数理与信息工程学院,浙江金华321004

出　　处：《数学研究》2012年第4期331-341,共11页Journal of Mathematical Study

基　　金：supported by the Scientific Research Fund of Zhejiang Provincial Education Department(Y201226078);The third author was supported partially by NSFC(11071223);ZJNSF(Z6090150)

摘　　要：图G的邻点可区别边染色是G的正常边染色,使得每一对相邻顶点有不同的颜色集合.G的邻点可区别边色数χ′_a(G)是使得G有一个k-邻点可区别边染色的最小正整数七.本文证明了:若G是围长至少为4且最大度至少为6的平面图,则χ′_a(G)≤△+2.An adjacent vertex distinguishing edge-colorings of graph G is a proper edge coloring of G such that any pair of adjacent vertices are incident to distinct sets of colors. The minimum number of colors required for an adjacent vertex distinguishing edge-coloring of G is denoted by x＇a（G）. In this paper, we prove that： if G is a planar graph with girth at least 4 and maximum degree at least 6, then x＇a（ G） △ ＋ 2.

关 键 词：邻点可区别边染色 平面图 最大度 围长 

分 类 号：O157.5[理学—数学]