Acyclic Coloring of Graphs of Maximum Degree Five: Nine Colors are Enough

Guillaume Fertin (1) , André Raspaud (2)

1 LINA - Laboratoire d'Informatique de Nantes Atlantique
2 LaBRI - Laboratoire Bordelais de Recherche en Informatique

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.

Mots clés: acyclic chromatic number; acyclic coloring algorithm; maximum degree 5; acyclic chromatic number

Domaines: Mathématique discrète [cs.DM]; Algorithme et structure de données [cs.DS]

Guillaume Fertin, André Raspaud. Acyclic Coloring of Graphs of Maximum Degree Five: Nine Colors are Enough. Information Processing Letters, 2008, 105 (2), pp.65-72. ⟨hal-00416567⟩