Results 1 to 10 of about 4,692 (164)
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
doaj +2 more sources
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
doaj +3 more sources
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
doaj +2 more sources
Bipartite Ramsey number pairs involving cycles
Discussiones Mathematicae Graph TheorySummary: 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
doaj +2 more sources
Degree Bipartite Ramsey Numbers [PDF]
Taiwanese Journal of Mathematics, 2021 Let $H\xrightarrow{s} G$ denote that any edge-coloring of $H$ by $s$ colors contains a monochromatic $G$. The degree Ramsey number $r_ (G;s)$ is defined to be $\min\{ (H):H\xrightarrow{s} G\}$, and the degree bipartite Ramsey number $br_ (G;s)$ is defined to be $\min\{ (H):H\xrightarrow{s} G\; \mbox{and} \; (H)=2\}$. In this note, we show that $r_
Wang, Ye, Li, Yusheng, Li, Yan
openaire +3 more sources
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 +2 more
doaj +1 more source
Asymptotic Bounds for Bipartite Ramsey Numbers [PDF]
The Electronic Journal of Combinatorics, 2001 The bipartite Ramsey number $b(m,n)$ is the smallest positive integer $r$ such that every (red, green) coloring of the edges of $K_{r,r}$ contains either a red $K_{m,m}$ or a green $K_{n,n}$. We obtain asymptotic bounds for $b(m,n)$ for $m \geq 2$ fixed and $n \rightarrow \infty$.
Caro, Yair, Rousseau, Cecil
openaire +2 more sources
AKCE International Journal of Graphs and Combinatorics, 2020 A sequence of graphs is a Ramsey sequence if for every positive integer k, the graph Gk is isomorphic to a proper subgraph of and for each positive integer k, there is an integer such that every red-blue coloring of Gn results in a monochromatic Gk. Some
Gary Chartrand, Ping Zhang
doaj +1 more source
Bipartite rainbow Ramsey numbers
Discrete Mathematics, 2004 This article introduces, proves the existence of, and computes some values of a new Ramsey number. Given a graph \(G\), with a subgraph \(H\), call an edge-coloring of \(G\) {rainbow} on \(H\) if the coloring assigns every edge of \(H\) its own color.
Eroh, Linda, Oellermann, Ortrud R.
openaire +2 more sources
Bipartite Ramsey numbers involving stars, stripes and trees
Electronic Journal of Graph Theory and Applications, 2013 The Ramsey number R(m, n) is the smallest integer p such that any blue-red colouring of the edges of the complete graph Kp forces the appearance of a blue Km or a red Kn.
Michalis Christou +2 more
doaj +1 more source