Results 21 to 30 of about 247,409 (283)
Large Book-Cycle Ramsey Numbers [PDF]
SIAM Journal on Discrete Mathematics, 2021 Let $B_n^{(k)}$ be the book graph which consists of $n$ copies of $K_{k+1}$ all sharing a common $K_k$, and let $C_m$ be a cycle of length $m$. In this paper, we first determine the exact value of $r(B_n^{(2)}, C_m)$ for $\frac{8}{9}n+112\le m\le \lceil\frac{3n}{2}\rceil+1$ and $n \geq 1000$.
Lin, Qizhong, Peng, Xing
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Ramsey Goodness and Beyond [PDF]
, 2007 In a seminal paper from 1983, Burr and Erdos started the systematic study of Ramsey numbers of cliques vs. large sparse graphs, raising a number of problems.
Nikiforov, Vladimir, Rousseau, Cecil C.
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Multicolor Size-Ramsey Number of Paths
پژوهشهای ریاضی, 2021 The size-Ramsey number of a graph denoted by is the smallest integer such that there is a graph with edges with this property that for any coloring of the edges of with colors, contains a monochromatic copy of.
Ramin Javadi, Meysam Miralaei
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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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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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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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