The total chromatic number of regular graphs of high degree

作     者：XIE DeZheng YANG WanNian 

作者机构：College of Mathematics and PhysicsChongqing UniversityChongqing 400044China 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2009年第52卷第8期

页      面：1743-1759页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by the Natural Science Foundation of Chongqing Science and Technology Commission(Grant No. 2007BB2123) 

主　　题：total chromatic number total coloring total coloring conjecture 05C15 

摘      要：The total chromatic number χT (G) of a graph G is the minimum number of colors needed to color the edges and the vertices of G so that incident or adjacent elements have distinct colors. We show that if G is a regular graph and d(G) ? 2 3 |V (G)|+ 23 6 , where d(G) denotes the degree of a vertex in G, then χT (G) ? d(G) + 2.