Algorithmic Aspects of Acyclic Edge Colorings

A proper coloring of the edges of a graph G is called acyclic if there is no 2-colored cycle in G. The acyclic edge chromatic number of G, denoted by a (G), is the least number of colors in an acyclic edge coloring of G. For certain graphs G, a (G) (G) + 2 where (G) is the maximum degree in G. It is known that a (G) + 2 for almost all -regular graphs, including all -regular graphs whose girth is at least c log . We prove that determining the acyclic edge chromatic number of an arbitrary graph is an NP-complete problem. For graphs G with sufficiently large girth in terms of (G), we present deterministic polynomial time algorithms that color the edges of G acyclically using at most (G) + 2 colors.

• Type: Journal
• Year: 2002
• Where: ALGORITHMICA
• Authors: Noga Alon, Ayal Zaks
• Keywords: -regular Graphs, Acyclic Edge, ALGORITHMICA 2002, Edge Chromatic Number