Results 1 to 10 of about 121 (114)
Ramsey theory and thermodynamics
Heliyon, 2023 Re-shaping of thermodynamics with the graph theory and Ramsey theory is suggested. Maps built of thermodynamic states are addressed. Thermodynamic states may be attainable and non-attainable by the thermodynamic process in the system of constant mass. We
Nir Shvalb +3 more
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Dynamics, 2023 Ramsey theory constitutes the dynamics of mechanical systems, which may be described as abstract complete graphs. We address a mechanical system which is completely interconnected by two kinds of ideal Hookean springs.
Nir Shvalb +3 more
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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 +2 more
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A Ramsey-Theory-Based Approach to the Dynamics of Systems of Material Points
DynamicsWe propose a Ramsey-theory-based approach for the analysis of the behavior of isolated mechanical systems containing interacting particles. The total momentum of the system in the frame of the center of masses is zero.
Edward Bormashenko, Nir Shvalb
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A Note on the Geometry of Closed Loops
Mathematics, 2023 In this paper, we utilize the Ramsey theory to investigate the geometrical characteristics of closed contours. We begin by examining a set of six points arranged on a closed contour and connected as a complete graph. We assign the downward-pointing edges
Nir Shvalb +3 more
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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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A note on the Ramsey numbers for theta graphs versus the wheel of order 5
AKCE International Journal of Graphs and Combinatorics, 2018 The study of exact values and bounds on the Ramsey numbers of graphs forms an important family of problems in the extremal graph theory. For a set of graphs S and a graph F , the Ramsey number R (S , F) is the smallest positive integer r such that for ...
Mohammed M.M. Jaradat +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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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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