Geodesic
A Tight Bound on the Set Chromatic Number
Discussiones Mathematicae. Graph Theory, Tome 33 (2013) no. 2, pp. 461-465.

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We provide a tight bound on the set chromatic number of a graph in terms of its chromatic number. Namely, for all graphs G, we show that χs(G) gt; ⌈log2 χ(G)⌉ + 1, where χs(G) and χ(G) are the set chromatic number and the chromatic number of G, respectively. This answers in the affirmative a conjecture of Gera, Okamoto, Rasmussen and Zhang.
Keywords: chromatic number, set coloring, set chromatic number, neighbor, distinguishing coloring 
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Sereni, Jean-Sébastien; Yilma, Zelealem B. A Tight Bound on the Set Chromatic Number. Discussiones Mathematicae. Graph Theory, Tome 33 (2013) no. 2, pp. 461-465. http://geodesic.mathdoc.fr/item/DMGT_2013_33_2_a17/

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[2] G. Chartrand, F. Okamoto, and P. Zhang, Neighbor-distinguishing vertex colorings of graphs, J. Combin. Math. Combin. Comput. 74 (2010) 223-251.

[3] R. Gera, F. Okamoto, C. Rasmussen, and P. Zhang, Set colorings in perfect graphs, Math. Bohem. 136 (2011) 61-68.