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Schreier sets in Ramsey theory [PDF]
Transactions of the American Mathematical Society, 2007 We show that Ramsey theory, a domain presently conceived to guarantee the existence of large homogeneous sets for partitions on k k
Farmaki, V., Negrepontis, S.
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Discrete & Computational Geometry, 1996 Let \((K_n, E_n)\) be a sequence of graphs in Euclidean spaces \(\mathbb{R}^n\). It is said to be edge-Ramsey if, for all \(r\geq 1\), a positive integer \(n= n(K, E, r)\) exists so that if \(m\geq n\), for any \(r\)-coloring of the edges of \(\mathbb{R}^m\), there is a graph \((L, F)\) in \(\mathbb{R}^m\) which is geometrically congruent to \((K_m ...
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Star-Critical Ramsey Numbers for Cycles Versus K4
Discussiones Mathematicae Graph Theory, 2021 Given three graphs G, H and K we write K → (G, H), if in any red/blue coloring of the edges of K there exists a red copy of G or a blue copy of H. The Ramsey number r(G, H) is defined as the smallest natural number n such that Kn → (G, H) and the star ...
Jayawardene Chula J. +2 more
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Constructions in Ramsey theory
Journal of the London Mathematical Society, 2018 We provide several constructions for problems in Ramsey theory. First, we prove a superexponential lower bound for the classical 4-uniform Ramsey number $r_4(5,n)$, and the same for the iterated $(k-4)$-fold logarithm of the $k$-uniform version $r_k(k+1,n)$.
Dhruv Mubayi, Andrew Suk
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Ultraproducts and Related Constructions
Mathematics, 2022 In this work, we survey some research directions in which the ultraproduct construction and methods based on ultrafilters play significant roles. Rather different areas of mathematics have been considered: topics we are reviewing here include some ...
Gábor Sági
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A strict upper bound for size multipartite Ramsey numbers of paths versus stars
Indonesian Journal of Combinatorics, 2017 Let $P_n$ represent the path of size $n$. Let $K_{1,m-1}$ represent a star of size $m$ and be denoted by $S_{m}$. Given a two coloring of the edges of a complete graph $K_{j \times s}$ we say that $K_{j \times s}\rightarrow (P_n,S_{m+1})$ if there is a ...
Chula Jayawardene, Lilanthi Samarasekara
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Journal of Combinatorial Theory, Series A, 1993 The following extension of the Erdős-Szekeres theorem is proved. If \(d,n\) are positive integers then there exists an integer \(N\) such that if \(f\) is an injection from \(\{1,2,\dots,N\}^ d\) into the reals then there is an \(n\times\cdots\times n\) subcube on which \(f\) is lexicographic and monotonic on each coordinate.
Peter C. Fishburn, Ronald L. Graham
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European Journal of Pragmatism and American Philosophy, 2022 One of Frank Ramsey’s crucial contributions to philosophy is his theory of belief. Ramsey deals with the notion of full belief in “Facts and Propositions,” as well as that of degrees of belief in “Truth and Probability.” In his posthumously published manuscript OnTruth, Ramsey analyses beliefs and emphasizes the essential role of agent’s actions in his
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Amenability and Ramsey theory [PDF]
Fundamenta Mathematicae, 2013 18 pages. Section 6 was expanded to contain a generalization of the main results to automorphism groups of Fraisse structures.
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Size multipartite Ramsey numbers for stripes versus small cycles
Electronic Journal of Graph Theory and Applications, 2016 For simple graphs $G_1$ and $G_2$, the size Ramsey multipartite number $m_j(G_1, G_2)$ is defined as the smallest natural number $s$ such that any arbitrary two coloring of the graph $K_{j \times s}$ using the colors red and blue, contains a red $G_1$ or
Chula Janak Jayawardene +3 more
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