On Total Colorings of Some Special 1-planar Graphs

作     者：Lin SUN Jian-liang WU Hua CAI 

作者机构：Department of Mathematics Changji University School of Mathematics Shandong University 

出 版 物：《Acta Mathematicae Applicatae Sinica》 (应用数学学报（英文版）)

年 卷 期：2017年第33卷第3期

页      面：607-618页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：Supported by the scientific research program of Xinjiang Uygur Autonomous Region grant 2016D01C012 the Scientific Research Program(XJEDU2016I046)of the Higher Education Institution of Xinjiang 

主　　题：1-planar graph total coloring discharging method girth r-minimal graph 

摘      要：A graph is 1-planar if it can be drawn on the plane so that each edge is crossed by at most one other edge. In this paper, we verify the total coloring conjecture for every 1-planar graph G if either △（G） ≥9 and g（G）≥ 4, or △（G） ≥ 7 and g（G）≥5, where △（G） is the maximum degree of G and g（G） is the girth of G.