点可区别全色数的一个界

J4 ›› 2011, Vol. 46 ›› Issue (6): 53-56.

点可区别全色数的一个界

强会英

兰州交通大学数理与软件工程学院, 甘肃兰州 730070

收稿日期:2010-05-17 出版日期:2011-06-16 发布日期:2011-12-19
作者简介:强会英(1968- ),女，副教授,硕士,研究方向为图论及其应用. Email:qhy2005ww@126.com
基金资助:
国家自然科学基金资助项目(10771091);甘肃省自然科学基金资助项目(1010RJZAO76);甘肃省”十一五”划课题2009(144)

A bound of the vertex-distinguishing total chromatic number of graphs

QIANG Hui-ying

College of Mathematics, Physics and Software Engineering, Lanzhou Jiaotong University, Lanzhou 730070, Gansu, China

Received:2010-05-17 Online:2011-06-16 Published:2011-12-19

摘要/Abstract

摘要：

图G的一个正常全染色被称作点可区别全染色, 如果G中任意两个点的色集合不同,其中每个点的色集合包含该点及其关联边的颜色。在点可区别全色数界(χ_vt(G)≤|V(G)|+2) 的基础上,应用概率的方法得到了阶数为n,且无孤立边的简单图G的点可区别全色数的一个较小上界。

关键词: 点可区别的全染色; 点可区别的全色数; Lovász 局部引理

Abstract:

A proper total coloring of the graph G is called vertex-distinguishing total coloring, if any two vertices have different color sets, where the color set of a vertex is the set composed of all colors of the vertex and the edges incident to it. On the base of the bound of vertex-distinguishing total chromatic number（ χ_vt( G)≤|V(G)|+2）. The new upper bound of vertex-distinguishing total chromatic number is obtained by way of probability.

Key words: vertex-distinguishing total coloring; vertex distinguishing total chromatic number; the Lovász local lemma

强会英. 点可区别全色数的一个界[J]. J4, 2011, 46(6): 53-56.

QIANG Hui-ying. A bound of the vertex-distinguishing total chromatic number of graphs[J]. J4, 2011, 46(6): 53-56.

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