Cyclic labellings with constraints at two distances.

Leese, R.A.; Noble, S.D.

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Acyclic sets in $k$ -majority tournaments.

Milans, Kevin G., Schreiber, Daniel H., West, Douglas B. (2011)

The Electronic Journal of Combinatorics [electronic only]

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Bounding the number of edges in permutation graphs.

Keevash, Peter, Loh, Po-Shen, Sudakov, Benny (2006)

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Star Coloring of Subcubic Graphs

T. Karthick, C.R. Subramanian (2013)

Discussiones Mathematicae Graph Theory

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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.