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Displaying similar documents to “Ramseyan properties of graphs.”

k -Ramsey classes and dimensions of graphs

Jan Kratochvíl (1995)

Commentationes Mathematicae Universitatis Carolinae

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In this note, we introduce the notion of k -Ramsey classes of graphs and we reveal connections to intersection dimensions of graphs.

Magic and supermagic dense bipartite graphs

Jaroslav Ivanco (2007)

Discussiones Mathematicae Graph Theory

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A graph is called magic (supermagic) if it admits a labelling of the edges by pairwise different (and consecutive) positive integers such that the sum of the labels of the edges incident with a vertex is independent of the particular vertex. In the paper we prove that any balanced bipartite graph with minimum degree greater than |V(G)|/4 ≥ 2 is magic. A similar result is presented for supermagic regular bipartite graphs.

Distinguishing graphs by the number of homomorphisms

Steve Fisk (1995)

Discussiones Mathematicae Graph Theory

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A homomorphism from one graph to another is a map that sends vertices to vertices and edges to edges. We denote the number of homomorphisms from G to H by |G → H|. If 𝓕 is a collection of graphs, we say that 𝓕 distinguishes graphs G and H if there is some member X of 𝓕 such that |G → X | ≠ |H → X|. 𝓕 is a distinguishing family if it distinguishes all pairs of graphs. We show that various collections of graphs are a distinguishing family.

Edge colorings and total colorings of integer distance graphs

Arnfried Kemnitz, Massimiliano Marangio (2002)

Discussiones Mathematicae Graph Theory

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An integer distance graph is a graph G(D) with the set Z of integers as vertex set and two vertices u,v ∈ Z are adjacent if and only if |u-v| ∈ D where the distance set D is a subset of the positive integers N. In this note we determine the chromatic index, the choice index, the total chromatic number and the total choice number of all integer distance graphs, and the choice number of special integer distance graphs.

On Generalized Sierpiński Graphs

Juan Alberto Rodríguez-Velázquez, Erick David Rodríguez-Bazan, Alejandro Estrada-Moreno (2017)

Discussiones Mathematicae Graph Theory

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In this paper we obtain closed formulae for several parameters of generalized Sierpiński graphs S(G, t) in terms of parameters of the base graph G. In particular, we focus on the chromatic, vertex cover, clique and domination numbers.

Generalized total colorings of graphs

Mieczysław Borowiecki, Arnfried Kemnitz, Massimiliano Marangio, Peter Mihók (2011)

Discussiones Mathematicae Graph Theory

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An additive hereditary property of graphs is a class of simple graphs which is closed under unions, subgraphs and isomorphism. Let P and Q be additive hereditary properties of graphs. A (P,Q)-total coloring of a simple graph G is a coloring of the vertices V(G) and edges E(G) of G such that for each color i the vertices colored by i induce a subgraph of property P, the edges colored by i induce a subgraph of property Q and incident vertices and edges obtain different colors. In this...

A metric for graphs

Vladimír Baláž, Jaroslav Koča, Vladimír Kvasnička, Milan Sekanina (1986)

Časopis pro pěstování matematiky

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