Anti-Ramsey numbers for graphs with independent cycles.
Jin, Zemin, Li, Xueliang (2009)
The Electronic Journal of Combinatorics [electronic only]
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Jin, Zemin, Li, Xueliang (2009)
The Electronic Journal of Combinatorics [electronic only]
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Albertson, Michael O., Chappell, Glenn G., Kierstead, H.A., Kündgen, André, Ramamurthi, Radhika (2004)
The Electronic Journal of Combinatorics [electronic only]
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Dzido, Tomasz, Kubale, Marek, Piwakowski, Konrad (2006)
The Electronic Journal of Combinatorics [electronic only]
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Mohar, Bojan, Škrekovski, Riste (1999)
The Electronic Journal of Combinatorics [electronic only]
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Ghebleh, Mohammad, Kral', Daniel, Norine, Serguei, Thomas, Robin (2006)
The Electronic Journal of Combinatorics [electronic only]
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Axenovich, Maria, Choi, JiHyeok (2010)
The Electronic Journal of Combinatorics [electronic only]
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Mubayi, Dhruv (2002)
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...
Gyárfás, András, Ruszinkó, Miklós, Sarközy, Gábor N., Szemerédi, Endre (2011)
The Electronic Journal of Combinatorics [electronic only]
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LeSaulnier, Timothy D., Stocker, Christopher, Wenger, Paul S., West, Douglas B. (2010)
The Electronic Journal of Combinatorics [electronic only]
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Wayne Goddard, Robert Melville (2017)
Open Mathematics
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We consider vertex colorings where the number of colors given to specified subgraphs is restricted. In particular, given some fixed graph F and some fixed set A of positive integers, we consider (not necessarily proper) colorings of the vertices of a graph G such that, for every copy of F in G, the number of colors it receives is in A. This generalizes proper colorings, defective coloring, and no-rainbow coloring, inter alia. In this paper we focus on the case that A is a singleton set....
Norine, Serguei, Zhu, Xuding (2008)
The Electronic Journal of Combinatorics [electronic only]
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Július Czap, Peter Šugerek, Jaroslav Ivančo (2016)
Discussiones Mathematicae Graph Theory
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An edge coloring φ of a graph G is called an M2-edge coloring if |φ(v)| ≤ 2 for every vertex v of G, where φ(v) is the set of colors of edges incident with v. Let 𝒦2(G) denote the maximum number of colors used in an M2-edge coloring of G. In this paper we determine 𝒦2(G) for trees, cacti, complete multipartite graphs and graph joins.
J. Czap, S. Jendrol’, J. Valiska (2017)
Discussiones Mathematicae Graph Theory
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Given three planar graphs F,H, and G, an (F,H)-WORM coloring of G is a vertex coloring such that no subgraph isomorphic to F is rainbow and no subgraph isomorphic to H is monochromatic. If G has at least one (F,H)-WORM coloring, then W−F,H(G) denotes the minimum number of colors in an (F,H)-WORM coloring of G. We show that (a) W−F,H(G) ≤ 2 if |V (F)| ≥ 3 and H contains a cycle, (b) W−F,H(G) ≤ 3 if |V (F)| ≥ 4 and H is a forest with Δ (H) ≥ 3, (c) W−F,H(G) ≤ 4 if |V (F)| ≥ 5 and H is...
Yuster, Raphael (2006)
The Electronic Journal of Combinatorics [electronic only]
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