On subgraphs induced by transversals in vertex-partitions of graphs.
Axenovich, Maria (2006)
The Electronic Journal of Combinatorics [electronic only]
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Displaying similar documents to “Avoiding rainbow induced subgraphs in vertex-colorings.”
On subgraphs induced by transversals in vertex-partitions of graphs.
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A Tight Bound on the Set Chromatic Number
Jean-Sébastien Sereni, Zelealem B. Yilma (2013)
Discussiones Mathematicae Graph Theory
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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) > ⌈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.