A Totally(Δ+1)-colorable 1-planar Graph with Girth at Least Five

作     者：Lin SUN Jian Liang WU Hua CAI 

作者机构：School of Mathematics Shandong University Ji'nan 250100 P. R. China Department of Mathematics Changji University Changji 831100 P. R. China 

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

年 卷 期：2016年第32卷第11期

页      面：1337-1349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 National Natural Science Foundation of China(Grant No.11271006) 

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

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 prove that every 1-planar graph G with maximum degree △（G） 〉 12 and girth at least five is totally （△（G）＋1）-colorable.