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A Tight Bound on the Set Chromatic Number

By Jean-Sébastien Sereni and Zelealem Yilma

Abstract

International audienceThe 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<sub>s</sub>(G) ≥ log<sub>2</sub>χ(G) + 1, where χ<sub>s</sub>(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

Topics: chromatic number, set coloring, set chromatic number, neighbor-distinguishing coloring, 05C15, [ INFO.INFO-DM ] Computer Science [cs]/Discrete Mathematics [cs.DM]
Publisher: University of Zielona Góra
Year: 2013
DOI identifier: 10.7151/dmgt.1679
OAI identifier: oai:HAL:hal-00624323v2
Provided by: Hal-Diderot

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