A Tight Bound on the Set Chromatic Number

Jean-Sébastien Sereni (1, 2) , Zelealem Yilma (1)

1 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications
2 KAM - Department of Applied Mathematics (KAM)

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 χ_s(G) ≥ log₂χ(G) + 1, where χ_s(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.

Mots clés: chromatic number; set coloring; set chromatic number; neighbor-distinguishing coloring

Domaines: Mathématique discrète [cs.DM]

Jean-Sébastien Sereni, Zelealem Yilma. A Tight Bound on the Set Chromatic Number. 2011. ⟨hal-00624323v1⟩