Acyclic edge coloring of triangle-free 1-planar graphs

Authors
Song, Wen Yao Miao, Lian Ying
Citation
Song, Wen Yao et Miao, Lian Ying, Acyclic edge coloring of triangle-free 1-planar graphs, Acta mathematica Sinica. English series (Print) , 31(10), 2015, pp. 1563-1570
Journal title
Acta mathematica Sinica. English series (Print) → ACNP
ISSN journal
14398516
Volume
31
Issue
10
Year of publication
2015
Pages
1563 - 1570
Database
ACNP
SICI code
Abstract
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 .. 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 .. a (G) . .(G)+22, if G is a triangle-free 1-planar graph.