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Keywords:

  • acyclic;
  • edge coloring;
  • outerplanar graph

Abstract

A proper edge coloring 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 χmath image(G), is the least number of colors in an acyclic edge coloring of G. In this paper, we determine completely the acyclic edge chromatic number of outerplanar graphs. The proof is constructive and supplies a polynomial time algorithm to acyclically color the edges of any outerplanar graph G using χmath image(G) colors. © 2009 Wiley Periodicals, Inc. J Graph Theory 64: 22–36, 2010