Results 1 to 10 of about 35 (35)
All finite sets are Ramsey in the maximum norm
Forum of Mathematics, Sigma, 2021 For two metric spaces $\mathbb X$ and $\mathcal Y$ the chromatic number $\chi ({{\mathbb X}};{{\mathcal{Y}}})$ of $\mathbb X$ with forbidden $\mathcal Y$ is the smallest k such that there is a colouring of the points of $\mathbb X$ with k colors that ...
Andrey Kupavskii, Arsenii Sagdeev
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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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Gallai-Ramsey Numbers for Rainbow S3+S_3^ + and Monochromatic Paths
Discussiones Mathematicae Graph Theory, 2022 Motivated by Ramsey theory and other rainbow-coloring-related problems, we consider edge-colorings of complete graphs without rainbow copy of some fixed subgraphs.
Li Xihe, Wang Ligong
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Singular Turán Numbers and Worm-Colorings
Discussiones Mathematicae Graph Theory, 2022 A subgraph G of H is singular if the vertices of G either have the same degree in H or have pairwise distinct degrees in H. The largest number of edges of a graph on n vertices that does not contain a singular copy of G is denoted by TS(n, G).
Gerbner Dániel +3 more
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A structure theorem for stochastic processes indexed by the discrete hypercube
Forum of Mathematics, Sigma, 2021 Let A be a finite set with , let n be a positive integer, and let $A^n$ denote the discrete $n\text {-dimensional}$ hypercube (that is, $A^n$ is the Cartesian product of n many copies of A).
Pandelis Dodos, Konstantinos Tyros
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Tower Gaps in Multicolour Ramsey Numbers
Forum of Mathematics, Sigma, 2023 Resolving a problem of Conlon, Fox and Rödl, we construct a family of hypergraphs with arbitrarily large tower height separation between their $2$ -colour and q-colour Ramsey numbers.
Quentin Dubroff +3 more
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Ramsey numbers of partial order graphs (comparability graphs) and implications in ring theory
Open Mathematics, 2020 For a partially ordered set (A,≤)(A,\le ), let GA{G}_{A} be the simple, undirected graph with vertex set A such that two vertices a≠b∈Aa\ne b\in A are adjacent if either a≤ba\le b or b≤ab\le a.
Badawi Ayman, Rissner Roswitha
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Zarankiewicz’s problem for semilinear hypergraphs
Forum of Mathematics, Sigma, 2021 A bipartite graph $H = \left (V_1, V_2; E \right )$ with $\lvert V_1\rvert + \lvert V_2\rvert = n$ is semilinear if $V_i \subseteq \mathbb {R}^{d_i}$ for some $d_i$ and the edge relation E consists of the pairs of points $(
Abdul Basit +4 more
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On the Restricted Size Ramsey Number Involving a Path P3
Discussiones Mathematicae Graph Theory, 2019 For any pair of graphs G and H, both the size Ramsey number ̂r(G,H) and the restricted size Ramsey number r*(G,H) are bounded above by the size of the complete graph with order equals to the Ramsey number r(G,H), and bounded below by e(G) + e(H) − 1 ...
Silaban Denny Riama +2 more
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Ramsey-type theorems for lines in 3-space [PDF]
Discrete Mathematics & Theoretical Computer Science, 2016 We prove geometric Ramsey-type statements on collections of lines in 3-space. These statements give guarantees on the size of a clique or an independent set in (hyper)graphs induced by incidence relations between lines, points, and reguli in 3-space ...
Jean Cardinal +2 more
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