Results 11 to 20 of about 21,406 (168)
Journal of Combinatorial Theory, Series B, 1993 The planar Ramsey number \(\text{PR}(k,\ell)\) \((k,\ell\geq 2)\) is the smallest integer \(n\) such that any planar graph on \(n\) vertices contains either a complete graph on \(k\) vertices or an independent set of size \(\ell\). We find exact values of \(\text{PR}(k,\ell)\) for all \(k\) and \(\ell\).
Richard Steinberg, Craig A. Tovey
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Size Ramsey number of bipartite graphs and bipartite Ramanujan graphs [PDF]
Transactions on Combinatorics, 2019 Given a graph $ G $, a graph $ F $ is said to be Ramsey for $ G $ if in every edge coloring of $F$ with two colors, there exists a monochromatic copy of $G$. The minimum number of edges of a graph $ F $ which is Ramsey for $ G $ is called the size-Ramsey
Ramin Javadi, Farideh Khoeini
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Discrete Mathematics, 1996 For a graph-theoretic parameter \(f\), an integer \(m\) and a graph \(H\), the mixed Ramsey number \(v(f;m;H)\) is the least positive integer \(p\) such that if \(G\) is any graph of order \(p\), then either \(f(G) \geq m\) or \(\overline G\) contains a subgraph isomorphic to \(H\).
Nirmala Achuthan +2 more
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Three-colour bipartite Ramsey number R_b(G_1,G_2,P_3)
Electronic Journal of Graph Theory and Applications, 2020 For simple bipartite graphs G1, G2, G3, the three-colour bipartite graph Ramsey number Rb(G1,G2,G3) is defined as the least positive integer n such that any 3-edge-colouring of Kn,n assures a monochromatic copy of Gi in the ith colour for some i, i ∈ {1 ...
R Lakshmi, D.G. Sindhu
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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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On Ramsey numbers of hedgehogs [PDF]
Combinatorics, Probability and Computing, 2019 AbstractThe hedgehog Ht is a 3-uniform hypergraph on vertices $1, \ldots ,t + \left({\matrix{t \cr 2}}\right)$ such that, for any pair (i, j) with 1 ≤ i < j ≤ t, there exists a unique vertex k > t such that {i, j, k} is an edge. Conlon, Fox and Rödl proved that the two-colour Ramsey number of the hedgehog grows polynomially in the number of its ...
Jacob Fox, Ray Li
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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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Multipartite Ramsey numbers for the union of stars
Electronic Journal of Graph Theory and Applications, 2022 Let s and k be positive integers with k ≥ 2 and G1, G2, …, Gk be simple graphs. The set multipartite Ramsey number, denoted by Ms(G1, G2, …, Gk), is the smallest positive integer c such that any k-coloring of the edges of Kc × s contains a monochromatic ...
I Wayan Palton Anuwiksa +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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A note on the Ramsey number for cycle with respect to multiple copies of wheels
Electronic Journal of Graph Theory and Applications, 2021 Let Kn be a complete graph with n vertices. For graphs G and H, the Ramsey number R(G, H) is the smallest positive integer n such that in every red-blue coloring on the edges of Kn, there is a red copy of graph G or a blue copy of graph H in Kn ...
I Wayan Sudarsana
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