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

Voir la notice de l'article dans European Digital Mathematics Library

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) > ⌈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.
Classification : 05C15
Mots-clés : chromatic number, set coloring, set chromatic number, neighbor, distinguishing coloring 
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Jean-Sébastien Sereni; Zelealem B. Yilma. A Tight Bound on the Set Chromatic Number. Discussiones Mathematicae Graph Theory, Tome 33 (2013) no. 2, p. 461. https://geodesic-test.mathdoc.fr/item/DMGT_2013__33_2_268003/