Star Coloring of Subcubic Graphs
Discussiones Mathematicae Graph Theory, Tome 33 (2013) no. 2, p. 373.

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A star coloring of an undirected graph G is a coloring of the vertices of G such that (i) no two adjacent vertices receive the same color, and (ii) no path on 4 vertices is bi-colored. The star chromatic number of G, χs(G), is the minimum number of colors needed to star color G. In this paper, we show that if a graph G is either non-regular subcubic or cubic with girth at least 6, then χs(G) ≤ 6, and the bound can be realized in linear time.
Classification : 05C15, 05C85
Mots-clés : vertex coloring, star coloring, subcubic graphs 
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T. Karthick; C.R. Subramanian. Star Coloring of Subcubic Graphs. Discussiones Mathematicae Graph Theory, Tome 33 (2013) no. 2, p. 373. https://geodesic-test.mathdoc.fr/item/DMGT_2013__33_2_268043/