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.
@article{bwmeta1.element.doi-10_7151_dmgt_1672,
author = {T. Karthick and C.R. Subramanian},
title = {Star Coloring of Subcubic Graphs},
journal = {Discussiones Mathematicae Graph Theory},
volume = {33},
year = {2013},
pages = {373-385},
zbl = {1293.05110},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_1672}
}
T. Karthick; C.R. Subramanian. Star Coloring of Subcubic Graphs. Discussiones Mathematicae Graph Theory, Tome 33 (2013) pp. 373-385. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1672/
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