A Tight Bound on the Set Chromatic Number

Jean-Sébastien Sereni 1 Zelealem Yilma 2
1 ORPAILLEUR - Knowledge representation, reasonning
Inria Nancy - Grand Est, LORIA - NLPKD - Department of Natural Language Processing & Knowledge Discovery
Abstract : The purpose of this note is to 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) ≥ log2χ(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.
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Jean-Sébastien Sereni, Zelealem Yilma. A Tight Bound on the Set Chromatic Number. Discussiones Mathematicae Graph Theory, University of Zielona Góra, 2013, 33 (2), pp.461--465. ⟨10.7151/dmgt.1679⟩. ⟨hal-00624323v2⟩

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