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Three-colour bipartite Ramsey number R_b(G_1,G_2,P_3) [PDF]

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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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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Bipartite Ramsey number pairs involving cycles

Discussiones Mathematicae Graph Theory
Summary: For bipartite graphs \(G_1, G_2,\ldots,G_k\), the bipartite Ramsey number \(b(G_1, G_2,\ldots, G_k)\) is the least positive integer \(b,\) so that any coloring of the edges of \(K_{b,b}\) with \(k\) colors, will result in a copy of \(G_i\) in the \(i\)th color, for some \(i\).
Ernst J. Joubert, Johannes Hattingh
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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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The m-bipartite Ramsey number of the K2,2 versus K6,6 [PDF]

Contributions to Mathematics, 2022
For the given bipartite graphs G 1 , . . . , G n , the bipartite Ramsey number BR ( G 1 , . . . , G n ) is the least positive integer b such that any complete bipartite graph K b,b having edges coloured with 1 , 2 , . . .
Yaser Rowshan
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The bipartite Ramsey numbers $BR(C_8, C_{2n})$ [PDF]

Discrete Mathematics & Theoretical Computer Science, 2021
For the given bipartite graphs $G_1,G_2,\ldots,G_t$, the multicolor bipartite Ramsey number $BR(G_1,G_2,\ldots,G_t)$ is the smallest positive integer $b$ such that any $t$-edge-coloring of $K_{b,b}$ contains a monochromatic subgraph isomorphic to $G_i ...
Mostafa Gholami, Yaser Rowshan
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Multicolour Bipartite Ramsey Number of Paths [PDF]

The Electronic Journal of Combinatorics, 2019
The k$-colour bipartite Ramsey number of a bipartite graph $H$ is the least integer $N$ for which every $k$-edge-coloured complete bipartite graph $K_{N,N}$ contains a monochromatic copy of $H$. The study of bipartite Ramsey numbers was initiated over 40
Matija Bucić, Shoham Letzter, B. Sudakov   +2 more
semanticscholar   +7 more sources

The m-bipartite Ramsey number BR_m(H₁,H₂)

Discussiones Mathematicae Graph Theory, 2022
In a (G1, G2) coloring of a graph G, every edge of G is in G1 or G2. For two bipartite graphs H1 and H2, the bipartite Ramsey number BR(H1, H2) is the least integer b ≥ 1, such that for every (G1, G2) coloring of the complete bipartite graph Kb,b ...
Yaser Rowshan
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A Proof of a Conjecture on Bipartite Ramsey Numbers B(2,2,3)

Mathematics, 2022
The bipartite Ramsey number B(n1,n2,…,nt) is the least positive integer b, such that any coloring of the edges of Kb,b with t colors will result in a monochromatic copy of Kni,ni in the i-th color, for some i, 1≤i≤t.
Yaser Rowshan, Mostafa Gholami, Stanford Shateyi   +2 more
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Degree Bipartite Ramsey Numbers [PDF]

Taiwanese Journal of Mathematics, 2019
Let $H\xrightarrow{s} G$ denote that any edge-coloring of $H$ by $s$ colors contains a monochromatic $G$. The degree Ramsey number $r_{\Delta}(G;s)$ is defined to be $\min\{\Delta(H):H\xrightarrow{s} G\}$, and the degree bipartite Ramsey number $br_ ...
Ye Wang, Yusheng Li, Yan Li
semanticscholar   +5 more sources