Résumé
A proper coloring of the vertices of a graph is called a star coloring if the union of every two color classes induces a star forest. The star chromatic number chi(S)(G) is the smallest number of colors required to obtain a star coloring of G. In this paper, we study the relationship between the star chromatic number chi(S)(G) and the maximum average degree Mad(G) of a graph G. We prove that:
1. If G is a graph with Mad(G) < 26/11, then chi(s)(G) <= 4.
2. If G is a graph with Mad(G) < 18/7 and girth at least 6, then chi(S)(G) <= 5.
3. If G is a graph with Mad(G) < 8/3 and girth at least 6, then chi(S)(G) <= 6.
These results are obtained by proving that such graphs admit a particular decomposition into a forest and some independent sets. (C) 2009 Wiley Periodicals, Inc. J Graph Theory 62: 201-219, 2009