Acyclic coloring of graphs of maximum degree five: Nine colors are enough

Authors:
Guillaume Fertin;André Raspaud
Affiliations:
LINA, FRE CNRS 2729, Université de Nantes, 2 rue de la Houssinière, BP 92208, F44322 Nantes Cedex 3, France;LaBRI UMR CNRS 5800, Université Bordeaux 1, 351 Cours de la Libération, F33405 Talence Cedex, France
Venue:
Information Processing Letters
Year:
2008

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Abstract

An acyclic coloring of a graph G is a coloring of its vertices such that: (i) no two neighbors in G are assigned the same color and (ii) no bicolored cycle can exist in G. The acyclic chromatic number of G is the least number of colors necessary to acyclically color G. In this paper, we show that any graph of maximum degree 5 has acyclic chromatic number at most 9, and we give a linear time algorithm that achieves this bound.