Acyclic Total Colorings of Planar Graphs without l Cycles

作     者：Xiang Yong SUN Jian Liang WU 

作者机构：School of Statistics and Mathematics Shandong Economic University Ji'nan 250014 P. R. China School of Mathematics and Systems Science Shandong University Ji'nan 250100 P. R. China 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2011年第27卷第7期

页      面：1315-1322页

核心收录：

学科分类：0711[理学-系统科学] 07[理学] 08[工学] 070105[理学-运筹学与控制论] 081101[工学-控制理论与控制工程] 0701[理学-数学] 071101[理学-系统理论] 0811[工学-控制科学与工程] 0823[工学-交通运输工程] 

基　　金：Supported by.National Natural Science Foundation of China (Grant Nos. 10971121, 10631070, 60673059) Acknowledgements We would like to thank the referees for providing some very helpful suggestions for revising this paper 

主　　题：Acyclic total coloring cycle planar graph 

摘      要：A proper total coloring of a graph G such that there are at least 4 colors on those vertices and edges incident with a cycle of G, is called acyclic total coloring. The acyclic total chromatic number of G is the least number of colors in an acyclic total coloring of G. In this paper, it is proved that the acyclic total chromatic number of a planar graph G of maximum degree at least k and without 1 cycles is at most △（G） ＋ 2 if （k, l） ∈ {（6, 3）, （7, 4）, （6, 5）, （7, 6）}.