Star Coloring of Graphs

Abstract : A star coloring of an undirected graph G is a proper vertex coloring of G (i.e., no two neighbors are assigned the same color) such that any path of length 3 in G is not bicolored. The star chromatic number of an undirected graph G, denoted by s(G), is the smallest integer k for which G admits a star coloring with k colors. In this paper, we give the exact value of the star chromatic number of different families of graphs such as trees, cycles, complete bipartite graphs, outerplanar graphs and 2-dimensional grids. We also study and give bounds for the star chromatic number of other families of graphs, such as planar graphs, hypercubes, d-dimensional grids (d \geq 3), d-dimensional tori (d \geq 2), graphs with bounded treewidth and cubic graphs. We end this study by two asymptotic results, where we prove that, when d tends to infinity, (i) there exist graphs G of maximum degree d such that s(G) = d^{3/2}/(log(d)^{1/2}) and (ii) for any graph G of maximum degree d, s(G) = O(d^{3/2}).
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Contributor : Guillaume Fertin <>
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Guillaume Fertin, André Raspaud, Bruce Reed. Star Coloring of Graphs. Journal of Graph Theory, Wiley, 2004, 47 (3), pp.163-182. ⟨hal-00307788⟩



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