Acyclic Edge Coloring of Triangle-free 1-planar Graphs

作     者：Wen Yao SONG Lian Ying MIAO 

作者机构：Institute of Mathematics China University of Mining and TechnologyXuzhou 

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

年 卷 期：2015年第31卷第10期

页      面：1563-1570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.11271365) 

主　　题：Acyclic chromatic index acyclic edge coloring 1-planar graph 

摘      要：A proper edge coloring of a graph G is acyclic if there is no 2-colored cycle in G. The acyclic chromatic index of G, denoted by X＇a（G）, is the least number of colors such that G has an acyclic edge coloring. 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, it is proved that X＇a（G） ≤△ A（G）＋ 22, if G is a triangle-free 1-planar graph.