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

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

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