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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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Restricted Size Ramsey Number Involving Matching and Graph of Order Five
Journal of Mathematical and Fundamental Sciences, 2020 Harary and Miller (1983) started the research on the (restricted) size Ramsey number for a pair of small graphs. They obtained the values for some pairs of small graphs with order not more than four.
Denny Riama Silaban +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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On minimal Ramsey graphs and Ramsey equivalence in multiple colours
, 2020 For an integer $q\ge 2$, a graph $G$ is called $q$-Ramsey for a graph $H$ if every $q$-colouring of the edges of $G$ contains a monochromatic copy of $H$. If $G$ is $q$-Ramsey for $H$, yet no proper subgraph of $G$ has this property then $G$ is called $q$
Clemens, Dennis +2 more
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Another View of Bipartite Ramsey Numbers
Discussiones Mathematicae Graph Theory, 2018 For bipartite graphs F and H and a positive integer s, the s-bipartite Ramsey number BRs(F,H) of F and H is the smallest integer t with t ≥ s such that every red-blue coloring of Ks,t results in a red F or a blue H.
Bi Zhenming, Chartrand Gary, Zhang Ping
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Single Atom and Two Atom Ramsey Interferometry with Quantized Fields [PDF]
, 2002 Implications of field quantization on Ramsey interferometry are discussed and general conditions for the occurrence of interference are obtained. Interferences do not occur if the fields in two Ramsey zones have precise number of photons. However in this
A. Rauschenbeutel +37 more
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Generalized Ramsey numbers for paths in 2-chromatic graphs
International Journal of Mathematics and Mathematical Sciences, 1986 Chung and Liu have defined the d-chromatic Ramsey number as follows. Let 1≤d≤c and let t=(cd). Let 1,2,…,t be the ordered subsets of d colors chosen from c distinct colors. Let G1,G2,…,Gt be graphs. The d-chromatic Ramsey number denoted by rdc(G1,G2,…,Gt)
R. Meenakshi, P. S. Sundararaghavan
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Restricted size Ramsey number for path of order three versus graph of order five
Electronic Journal of Graph Theory and Applications, 2017 Let $G$ and $H$ be simple graphs. The Ramsey number for a pair of graph $G$ and $H$ is the smallest number $r$ such that any red-blue coloring of edges of $K_r$ contains a red subgraph $G$ or a blue subgraph $H$.
Denny Riama Silaban +2 more
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, 2016 The purpose of this paper is to introduce the idea of triangular Ramsey numbers and provide values as well as upper and lower bounds for them. To do this, the combinatorial game Mines is introduced; after some necessary theorems about triangular sets are proved. This game is easy enough that young children are able to play. The most basic variations of
Chaney, Zachary +3 more
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Sidon–Ramsey and $$B_{h}$$-Ramsey numbers
Boletín de la Sociedad Matemática MexicanaAbstractFor a given positive integer k, the Sidon–Ramsey number $${{\,\textrm{SR}\,}}(k)$$ SR ( k ) is defined as the minimum ...
Manuel A. Espinosa-García +3 more
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