图的邻点强可区别全色数的一个上界  

An Upper Bound of the Adjacent-vertex-strong-distinguishing Total Chromatic Number of Graphs

作　　者：强会英[1] 王洪申[2] 

机构地区：[1]兰州交通大学数理与软件工程学院,兰州甘肃730070 [2]兰州理工大学机电工程学院,兰州甘肃730050

出　　处：《数学进展》2013年第6期801-805,共5页Advances in Mathematics（China）

基　　金：国家自然科学基金(No.11161028);甘肃省自然科学基金(No.1010RJZA076);甘肃省"十一五"规划课题(No.2009(144))

摘　　要：图G的一个正常金染色被称作邻点强可区别全染色,如果G中任意两个相邻点的色集合不同,其中每个点的色集合包含该点及其关联边和相邻点的颜色.在图的邻点强可区别全色数界(x_(ast)(G)≤2△(G)+1)的基础上,应用概率的方法得到了最大度不小于3,且无孤立边的简单图G的邻点强可区别全色数的又一个新上界.A proper total coloring of the graph G is called adjacent-vertex-strong-distin- guishing total coloring, if any two adjacent vertices have different color sets, where the color set of a vertex u is the set composed of all colors of u and the edges and vertices incident to u. On the base of the bound of adjacent-vertex-strong-distinguishing total chromatic number（χast（G）≤2△（G）＋1）, the new upper bounds of the adjacent-vertex-strong-distinguishing total chromatic number of the graph G is obtained by the way of probability, where G is a simple graph with no isolated edge and △（G）≥ 3.

关 键 词：邻点强可区别全染色 邻点强可区别的全色数 一般形式的Lovasz局部引理 

分 类 号：O157.5[理学—数学]