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 “Online coloring known graphs.”
On subgraphs induced by transversals in vertex-partitions of graphs.
A note on graph coloring extensions and list-colorings.
Axenovich, Maria (2003)
The Electronic Journal of Combinatorics [electronic only]
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How to find overfull subgraphs in graphs with large maximum degree. II.
Niessen, Thomas (2001)
The Electronic Journal of Combinatorics [electronic only]
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Avoiding rainbow induced subgraphs in vertex-colorings.
Axenovich, Maria, Martin, Ryan (2008)
The Electronic Journal of Combinatorics [electronic only]
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The order of monochromatic subgraphs with a given minimum degree.
Caro, Yair, Yuster, Raphael (2003)
The Electronic Journal of Combinatorics [electronic only]
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Computation of the vertex Folkman numbers and .
Nedialkov, Evgeni, Nenov, Nedyalko (2002)
The Electronic Journal of Combinatorics [electronic only]
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Rainbow -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.
-free graphs of large minimum degree.
Alon, Noga, Sudakov, Benny (2006)
The Electronic Journal of Combinatorics [electronic only]
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Star coloring high girth planar graphs.
Timmons, Craig (2008)
The Electronic Journal of Combinatorics [electronic only]
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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...
Contraction and treewidth lower bounds.
Bodlaender, Hans L., Wolle, Thomas, Koster, Arie M.C.A. (2006)
Journal of Graph Algorithms and Applications
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On the Rainbow Vertex-Connection
Xueliang Li, Yongtang Shi (2013)
Discussiones Mathematicae Graph Theory
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A vertex-colored graph is rainbow vertex-connected if any two vertices are connected by a path whose internal vertices have distinct colors. The rainbow vertex-connection of a connected graph G, denoted by rvc(G), is the smallest number of colors that are needed in order to make G rainbow vertexconnected. It was proved that if G is a graph of order n with minimum degree δ, then rvc(G) < 11n/δ. In this paper, we show that rvc(G) ≤ 3n/(δ+1)+5 for [xxx] and n ≥ 290, while rvc(G) ≤ 4n/(δ...