The 4-Acyclic Edge Coloring of Graphs with Large Girths
Yuwen Wu, Yan Xia · Journal of Applied Mathematics and Physics · 2015
A proper edge coloring of a graph is acyclic, if every cycle of the graph has at least 3 colors. Let r be a positive integer. An edge coloring is r-acyclic if it is proper and every cycle C has at least colors. The r-acyclic edge chromatic number of a graph G is the minimum number of colors needed for any r-acyclic edge coloring of G. When r=4, the result of this paper is that the 4-acyclic chromatic number of a graph with maximum degree Δ and girth is less than 18Δ. Furthermore, if the girth of graph G is at least , then .