Results 11 to 20 of about 787 (166)
Landauer Principle and Einstein Synchronization of Clocks: Ramsey Approach [PDF]
EntropyWe introduce a synchronization procedure for clocks based on the Einstein–Landauer framework. Clocks are modeled as discrete, macroscopic devices operating at a thermal equilibrium temperature T.
Edward Bormashenko, Michael Nosonovsky
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Andrásfai and Vega graphs in Ramsey–Turán theory [PDF]
Journal of Graph Theory, 2021 AbstractGiven positive integers , we let denote the maximum number of edges in a triangle‐free graph on vertices with . In the early 1960s, Andrásfai conjectured that for the function is piecewise quadratic with critical values at for . We confirm that this is indeed the case whenever is slightly larger than a critical value, thus determining ...
Tomasz Luczak 0001 +2 more
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A Ramsey–Turán theory for tilings in graphs
Random Structures & Algorithms, 2023 AbstractFor a ‐vertex graph and an ‐vertex graph , an ‐tiling in is a collection of vertex‐disjoint copies of in . For , the ‐independence number of , denoted , is the largest size of a ‐free set of vertices in . In this article, we discuss Ramsey–Turán‐type theorems for tilings where one is interested in minimum degree and independence number ...
Jie Han 0002 +3 more
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The Ramsey theory of Henson graphs
Journal of Mathematical Logic, 2022 Analogues of Ramsey’s Theorem for infinite structures such as the rationals or the Rado graph have been known for some time. In this context, one looks for optimal bounds, called degrees, for the number of colors in an isomorphic substructure rather than one color, as that is often impossible.
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On two problems in graph Ramsey theory [PDF]
Combinatorica, 2012 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. The Ramsey number r(H) of a graph H is the least positive integer N such that every two-coloring of the edges of the complete graph $K_N ...
David Conlon, Jacob Fox, Benny Sudakov
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On-line Ramsey Theory for Bounded Degree Graphs [PDF]
The Electronic Journal of Combinatorics, 2011 When graph Ramsey theory is viewed as a game, "Painter" 2-colors the edges of a graph presented by "Builder". Builder wins if every coloring has a monochromatic copy of a fixed graph $G$. In the on-line version, iteratively, Builder presents one edge and Painter must color it. Builder must keep the presented graph in a class ${\cal H}$.
Jane Butterfield +5 more
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Anti-Ramsey theory on complete bipartite graphs [PDF]
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 this bound is sharp. We also define and compute some new anti-Ramsey numbers.
Stephan Cho +3 more
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Graph Ramsey theory and the polynomial hierarchy [PDF]
Proceedings of the thirty-first annual ACM symposium on Theory of Computing, 1999 One of the usual ways to formulate Ramsey theory statements for graphs is by using arrowing notation. \(F\to (G,H)\) means that if the edges of \(F\) are colored red and blue, either a red \(G\) or a blue \(H\) must occur. \textit{S. A. Burr} [Algorithms Comb.
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Turán and Ramsey problems for alternating multilinear maps
Discrete Analysis, 2023 Turán and Ramsey problems for alternating multilinear maps, Discrete Analysis 2023:12, 22 pp. Ramsey's theorem (in its finite version) states that for every positive integer $k$ there exists a positive integer $n$ such that every graph with $n$ vertices
Youming Qiao
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On Small Balanceable, Strongly-Balanceable and Omnitonal Graphs
Discussiones Mathematicae Graph Theory, 2022 In Ramsey Theory for graphs we are given a graph G and we are required to find the least n0 such that, for any n ≥ n0, any red/blue colouring of the edges of Kn gives a subgraph G all of whose edges are blue or all are red.
Caro Yair, Lauri Josef, Zarb Christina
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