Geodesic
Star Coloring of Subcubic Graphs
Discussiones Mathematicae. Graph Theory, Tome 33 (2013) no. 2, pp. 373-385

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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.
Keywords: vertex coloring, star coloring, subcubic graphs 
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Karthick, T.; Subramanian, C.R. Star Coloring of Subcubic Graphs. Discussiones Mathematicae. Graph Theory, Tome 33 (2013) no. 2, pp. 373-385. http://geodesic.mathdoc.fr/item/DMGT_2013_33_2_a10/