Results 121 to 130 of about 1,125 (159)

An Anti-Ramsey Theorem

Combinatorica, 2002
The Turán number \(t_p(n)\) is the maximum size of a graph with \(n\) vertices without subgraphs isomorphic to the complete graph \(K_p\). A subgraph of \(K_n\) is called totally multicoloured (with respect to an edge colouring of \(K_n\)) if all edges have different colours. Let \(h_r(n)\) be the minimum number of colours so that any edge colouring of
Montellano-Ballesteros, J. J., Neumann-Lara, V.   +1 more
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Ramsey’s Theorem

2013
Frank Plumpton Ramsey was an extraordinary man. He was born in 1903 in Cambridge as the elder son of A.S. Ramsey who was a mathematician and President of Magdalene College. His younger brother Michael went on to become Archbishop of Canterbury.
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Ramsey’s Theorem

2001
In 1930 Frank Plumpton Ramsey had written a paper On a problem in formal logic which initiated a part of discrete mathematics nowadays known as Ramsey Theory. At about the same time B.L. van der Waerden (1927) proved his famous Ramsey-type result on arithmetical progressions. A few years later Ramsey’s theorem was rediscovered by P.
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Ultrafilters and multidimensional Ramsey Theorems

Combinatorica, 1989
Simultaneous generalizations of Ramsey's theorem and single dimension Ramsey-type theorems are proved using ultrafilters on the set N of natural numbers which have certain special properties. The main result utilizes a ``combinatorically large ultrafilter'' to obtain a very strong generalization of Ramsey's theorem and Van der Waerden's theorem ...
Bergelson, V., Hindman, N.
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Ramsey’s theorem and König’s Lemma

Archive for Mathematical Logic, 2006
Let \([X]^n\) denote the set of \(n\)-element subsets of \(X\). For natural numbers \(n\), \(k\), Ramsey's theorem \(\text{RT}^n_k\) states: For any infinite set \(X\) and map \(F: [X]^n\to k\), there is an infinite subset \(Y\subseteq X\) such that the restriction of \(F\) to \([Y]^n\) is constant.
Forster, T. E., Truss, J. K.
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Overture: Ramsey’s Theorem

2012
In this chapter, the following theorem—which can be considered as the nucleus of Ramsey Theory—will be discussed in great detail.
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Ramsey’s theorem

2022
Damir D. Dzhafarov, Carl Mummert
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Sparse Ramsey Theorems

2013
Sparse Ramsey theorems for graphs originated with investigations of graphs having large chromatic number and high girth (where the girth of a graph is the length of the smallest cycle in G). Note that this can be viewed as a special kind of restricted graph Ramsey problem.
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Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators

Nature Machine Intelligence, 2021
Lu Lu, Pengzhan Jin, Guofei Pang
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Experimental quantum key distribution certified by Bell's theorem

Nature, 2022
David Nadlinger, C j Ballance, Kirill Ivanov   +2 more
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