Discussiones Mathematicae Graph Theory 33(2) (2013) 373-385
doi: 10.7151/dmgt.1672

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Star Coloring of Subcubic Graphs

T. Karthick and C.R. Subramanian

Indian Statistical Institute, Chennai Centre
Chennai- 600 113, India


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

2010 Mathematics Subject Classification: 05C15, 05C85.


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Received 7 December 2011
Revised 23 May 2012
Accepted 23 May 2012