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has been cited by the following article:

• TITLE: The 4-Acyclic Edge Coloring of Graphs with Large Girths

  AUTHORS: Yuwen Wu, Yan Xia

  KEYWORDS: Girth, Edge Coloring, Acyclic Edge Coloring, Lovászlocal Lemma

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.3 No.12, December 16, 2015

  ABSTRACT: 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 Gis 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 Gis at least , then .