On subgraphs induced by transversals in vertex-partitions of graphs.
Axenovich, Maria (2006)
The Electronic Journal of Combinatorics [electronic only]
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Axenovich, Maria (2006)
The Electronic Journal of Combinatorics [electronic only]
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Axenovich, Maria, Martin, Ryan (2008)
The Electronic Journal of Combinatorics [electronic only]
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Caro, Yair, Yuster, Raphael (2003)
The Electronic Journal of Combinatorics [electronic only]
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Yuster, Raphael (2006)
The Electronic Journal of Combinatorics [electronic only]
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Timmons, Craig (2008)
The Electronic Journal of Combinatorics [electronic only]
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Collins, Karen L., Trenk, Ann N. (2006)
The Electronic Journal of Combinatorics [electronic only]
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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...
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.
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....
Nedialkov, Evgeni, Nenov, Nedyalko (2002)
The Electronic Journal of Combinatorics [electronic only]
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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...
Poppy Immel, Paul S. Wenger (2017)
Discussiones Mathematicae Graph Theory
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A distinguishing coloring of a graph G is a coloring of the vertices so that every nontrivial automorphism of G maps some vertex to a vertex with a different color. The distinguishing number of G is the minimum k such that G has a distinguishing coloring where each vertex is assigned a color from {1, . . . , k}. A list assignment to G is an assignment L = {L(v)}v∈V (G) of lists of colors to the vertices of G. A distinguishing L-coloring of G is a distinguishing coloring of G where the...
Alishahi, Meysam, Taherkhani, Ali, Thomassen, Carsten (2011)
The Electronic Journal of Combinatorics [electronic only]
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Yuehua Bu, Ko-Wei Lih, Weifan Wang (2011)
Discussiones Mathematicae Graph Theory
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An adjacent vertex distinguishing edge-coloring of a graph G is a proper edge-coloring o G such that any pair of adjacent vertices are incident to distinct sets of colors. The minimum number of colors required for an adjacent vertex distinguishing edge-coloring of G is denoted by χ'ₐ(G). We prove that χ'ₐ(G) is at most the maximum degree plus 2 if G is a planar graph without isolated edges whose girth is at least 6. This gives new evidence to a conjecture proposed in [Z. Zhang, L. Liu,...