Results 71 to 80 of about 787 (166)
A multidimensional Ramsey theorem
Discrete AnalysisA multidimensional Ramsey theorem, Discrete Analysis 2024:21, 10 pp. Ramsey's theorem, the founding result of Ramsey theory, states that for every pair of positive integers $r$ and $k$ there exists $n$ such that if the edges of the complete graph $K_n ...
Antonio Girão +2 more
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Ramsey theory and strength of graphs
A numbering $f$ of a graph $G$ of order $n$ is a labeling that assigns distinct elements of the set $\left\{ 1,2,\ldots ,n\right\} $ to the vertices of $G$, where each $uv\in E\left( G\right) $ is labeled $f\left( u\right) +f\left( v\right) $. The strength $\mathrm{str}\left( G\right) $ of $G$ is defined by $\mathrm{str}\left( G\right) =\min \left ...
Ichishima, Rikio +2 more
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Monochromatic Sums and Products of Polynomials
Discrete AnalysisMonochromatic sums and products of polynomials, Discrete Analysis 2024:5, 7 pp. An early result in Ramsey theory, Schur's theorem, states that if the positive integers are finitely coloured, then there will always be $x$ and $y$ such that $x,y$ and $x ...
Ryan Alweiss
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Fermat Principle, Ramsey Theory and Metamaterials. [PDF]
Materials (Basel), 2023 Frenkel M, Shoval S, Bormashenko E.
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A natural generalisation in graph Ramsey theory
, 2017 In this note we study graphs $G_r$ with the property that every colouring of $E(G_r)$ with $r+1$ colours admits a copy of some graph $H$ using at most $r$ colours. For $1\le r\le e(H)$ such graphs occur naturally at intermediate steps in the synthesis of a $2$-colour Ramsey graph $G_1\longrightarrow H$.
Haupt, Alexander, Reding, Damian
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Shannon Entropy of Ramsey Graphs with up to Six Vertices. [PDF]
Entropy (Basel), 2023 Frenkel M, Shoval S, Bormashenko E.
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Ramsey Theory and Knowledge Graphs
, 2023 The purpose of this paper is to provide certain notes on how Knowledge Graphs can be analyzed and mined apart from the common Machine Learning algorithms or standard graph-based approaches. The current paper analyses some of the Ramsey-type results obtained for (mostly) geometrical graphs. Then a connection to the Knowledge Graphs problems is built. As
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Problems in extremal graph theory and Euclidean Ramsey theory.
, 2019 This thesis addresses problems of three types. The first type is finding extremal numbers for unions of graphs, each with a colour-critical edge (joint work with V. Nikiforov). In 1968, Simonovits found extremal numbers $ex(n,H)$ for graphs with a colour-critical edge for large $n$ (without specifying how large).
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A generalization of Ramsey theory for graphs
Discrete Mathematics, 1978 K. M. Chung, C. L. Liu 0001
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