Results 31 to 40 of about 157,308 (292)
, 2022 AbstractRamsey theory is a branch of combinatorics that asks questions of the form: How large must a set be so that if it is divided into subsets, at least one subset has a certain property? Results in Ramsey theory are difficult to prove and there remain many open problems.
Michael A. Henning, Jan H. van Vuuren
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Nonstandard Methods in Ramsey Theory and Combinatorial Number Theory [PDF]
, 2017 The goal of this present manuscript is to introduce the reader to the nonstandard method and to provide an overview of its most prominent applications in Ramsey theory and combinatorial number theory.Comment: 126 pages.
Di Nasso, Mauro +2 more
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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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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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Short proofs of some extremal results [PDF]
, 2013 We prove several results from different areas of extremal combinatorics, giving complete or partial solutions to a number of open problems. These results, coming from areas such as extremal graph theory, Ramsey theory and additive combinatorics, have ...
Beck +11 more
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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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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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Anti-Ramsey theory on complete bipartite graphs
AKCE International Journal of Graphs and Combinatorics, 2020 We consider quadruples of positive integers with and such that every proper edge-coloring of the complete bipartite graph contains a rainbow subgraph. We show that every such quadruple with and satisfies this property and find an infinite sequence where ...
Stephan Cho +3 more
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On two problems in graph Ramsey theory [PDF]
, 2010 We study two classical problems in graph Ramsey theory, that of determining the Ramsey number of bounded-degree graphs and that of estimating the induced Ramsey number for a graph with a given number of vertices.
A. Thomason +36 more
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Lines in Euclidean Ramsey theory [PDF]
, 2018 Let $\ell_m$ be a sequence of $m$ points on a line with consecutive points of distance one. For every natural number $n$, we prove the existence of a red/blue-coloring of $\mathbb{E}^n$ containing no red copy of $\ell_2$ and no blue copy of $\ell_m$ for ...
Conlon, David, Fox, Jacob
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