Displaying similar documents to “On subgraphs induced by transversals in vertex-partitions of graphs.”

Rainbow H -factors.

Yuster, Raphael (2006)

The Electronic Journal of Combinatorics [electronic only]

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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.

Vertex Colorings without Rainbow Subgraphs

Wayne Goddard, Honghai Xu (2016)

Discussiones Mathematicae Graph Theory

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Given a coloring of the vertices of a graph G, we say a subgraph is rainbow if its vertices receive distinct colors. For a graph F, we define the F-upper chromatic number of G as the maximum number of colors that can be used to color the vertices of G such that there is no rainbow copy of F. We present some results on this parameter for certain graph classes. The focus is on the case that F is a star or triangle. For example, we show that the K3-upper chromatic number of any maximal...

Worm Colorings

Wayne Goddard, Kirsti Wash, Honghai Xu (2015)

Discussiones Mathematicae Graph Theory

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Given a coloring of the vertices, we say subgraph H is monochromatic if every vertex of H is assigned the same color, and rainbow if no pair of vertices of H are assigned the same color. Given a graph G and a graph F, we define an F-WORM coloring of G as a coloring of the vertices of G without a rainbow or monochromatic subgraph H isomorphic to F. We present some results on this concept especially as regards to the existence, complexity, and optimization within certain graph classes....