Ramsey's theorem

Known as: R(5, 5), Ramsey number, Ramsey theorem 
In combinatorial mathematics, Ramsey's theorem states that one will find monochromatic cliques in any edge labelling (with colours) of a sufficiently… (More)
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2009
2009
We study the effective and proof-theoretic content of the polarized Ramsey’s theorem, a variant of Ramsey’s theorem obtained by… (More)
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2009
2009
It was shown by Cholak, Jockusch, and Slaman that every computable 2-coloring of pairs admits an infinite low2 homogeneous set H… (More)
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2009
2009
The Rainbow Ramsey Theorem is essentially an “anti-Ramsey” theorem which states that certain types of colorings must be injective… (More)
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Highly Cited
2007
Highly Cited
2007
We investigate the complexity of various combinatorial theorems about linear and partial orders, from the points of view of… (More)
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1985
1985
An edge-coloring of a graph is a partition of the set of edges into color-classes such that no two edges in the same class are… (More)
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Highly Cited
1983
Highly Cited
1983
The size Ramsey number i ( G ) of a graph G is the smallest integer i such that there is a graph F of i edges with the property… (More)
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1979
1979
We prove a Ramsey theorem for trees. The infinite version of this theorem GUI be stated: if T is a rooted tree of infinite height… (More)
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1979
1979
A short proof is given of the following known result. For all k, r, t there exists n so that if the /-spaces of an n-space are… (More)
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Highly Cited
1978
Highly Cited
1978
Let i2 denote the class of all graphs G which satisfy G-(Gl, GE). As a way of measuring r inimality for members of P, we define… (More)
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Highly Cited
1977
Highly Cited
1977
The probabilisrk mefkod is a powerful technique for approaching asymptotic combinatorial problems. This paper considers an… (More)
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