Results 171 to 180 of about 1,298 (200)
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Ramsey Theory and Bandwidth of Graphs
Graphs and Combinatorics, 2001zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zoltán Füredi, Douglas B. West
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A conjecture of Erdős on graph Ramsey numbers
Advances in Mathematics, 2011 The Ramsey number r(G) of a graph G is the minimum N such that every red–blue coloring of the edges of the complete graph on N vertices contains a monochromatic copy of G.
Benny Sudakov
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Ramsey theory for graph connectivity
Journal of Graph Theory, 1983Abstractrc(k) Denotes the smallest integer such that any c‐edge‐coloring of the rc(k) vertex complete graph has a monochromatic k‐connected subgraph. For any c, k ≧ 2, we show 2c(k – 1) + 1 ≦ rc(k) < 10/3 c(k – 1) + 1, and further that 4(k – 1) + 1 ≧ r2(k) < (3 + √ (k – 1) + 1.
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Generalized ramsey theory for graphs VII: Ramsey numbers for multigraphs and networks
Networks, 1978AbstractRamsey problems are examined for the different varieties of graphs and digraphs, with and without loops and multiple edges, and even for networks. In every case, the resulting Ramsey number either fails to exist, or has a trivial value, or equals the value for the underlying graph or digraph.
Frank Harary, Allen J. Schwenk
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Ars Comb., 2003
The authors survey results in induced graph Ramsey theory and prove quite a few constructive upper bounds without using probabilistic method (needless to say, these are much weaker than the bounds obtained nonconstructively). For two simple graphs \(G\) and \(H\) let \(r^*(G,H)\) (\(r^*(G)=r^*(G,G)\)) be the smallest number of vertices in a simple ...
Marcus Schaefer 0001, Pradyut Shah
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The authors survey results in induced graph Ramsey theory and prove quite a few constructive upper bounds without using probabilistic method (needless to say, these are much weaker than the bounds obtained nonconstructively). For two simple graphs \(G\) and \(H\) let \(r^*(G,H)\) (\(r^*(G)=r^*(G,G)\)) be the smallest number of vertices in a simple ...
Marcus Schaefer 0001, Pradyut Shah
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Graph Parameters and Ramsey Theory
2018Ramsey’s Theorem tells us that there are exactly two minimal hereditary classes containing graphs with arbitrarily many vertices: the class of complete graphs and the class of edgeless graphs. In other words, Ramsey’s Theorem characterizes the graph vertex number in terms of minimal hereditary classes where this parameter is unbounded.
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2005
In this chapter we set out from a type of problem which, on the face of it, appears to be similar to the theme of Chapter 7: what kind of substructures are necessarily present in every large enough graph?
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In this chapter we set out from a type of problem which, on the face of it, appears to be similar to the theme of Chapter 7: what kind of substructures are necessarily present in every large enough graph?
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Coloring number and on-line Ramsey theory for graphs and hypergraphs
Combinatorica, 2009zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hal A. Kierstead, Goran Konjevod
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Graphs and Orders in Ramsey Theory and in Dimension Theory
1985The purpose of this paper is to present a concise and relatively self contained treatment of recent results linking partially ordered sets with topics more traditionally associated with graph theory and combinatorics: Ramsey theory and chromatic graph theory.
M. Paoli, W. T. Trotter, J. W. Walker
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Generalized ramsey theory for graphs - a survey
1974Almost nonexistent a few years ago, the field of generalized Ramsey theory for graphs is now being pursued very actively and with remarkable success. This survey paper will emphasize the following class of problems: Given graphs G1, ..., Gc, determine or estimate the Ramsey number r(G1, ..., Gc), the smallest number p such that if the lines of a ...
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