Results 21 to 30 of about 21,746 (178)
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
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Discrete Mathematics, 2009 For bipartite graphs \(B_1\) and \(B_2\), the \textit{size bipartite Ramsey number} \(\widehat{br}(B_1, B_2)\) is the size of the smallest bipartite graph \(B\) such that in any \(2\)-coloring of the edges of \(B\) there will be copy of \(B_1\) in the first color or a copy of \(B_2\) in the second color.
Sun, Yuqin, Li, Yusheng
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Extremal results in sparse pseudorandom graphs [PDF]
, 2012 Szemer\'edi's regularity lemma is a fundamental tool in extremal combinatorics. However, the original version is only helpful in studying dense graphs.
Conlon, David, Fox, Jacob, Zhao, Yufei
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The critical window for the classical Ramsey-Tur\'an problem [PDF]
, 2012 The first application of Szemer\'edi's powerful regularity method was the following celebrated Ramsey-Tur\'an result proved by Szemer\'edi in 1972: any K_4-free graph on N vertices with independence number o(N) has at most (1/8 + o(1)) N^2 edges.
A. Frieze +42 more
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A General Lower Bound on Gallai-Ramsey Numbers for Non-Bipartite Graphs
Theory and Applications of Graphs, 2018 Given a graph $H$ and a positive integer $k$, the $k$-color Gallai-Ramsey number $gr_{k}(K_{3} : H)$ is defined to be the minimum number of vertices $n$ for which any $k$-coloring of the complete graph $K_{n}$ contains either a rainbow triangle or a ...
Colton Magnant
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On size multipartite Ramsey numbers for stars versus paths and cycles
Electronic Journal of Graph Theory and Applications, 2017 Let $K_{l\times t}$ be a complete, balanced, multipartite graph consisting of $l$ partite sets and $t$ vertices in each partite set. For given two graphs $G_1$ and $G_2$, and integer $j\geq 2$, the size multipartite Ramsey number $m_j(G_1,G_2)$ is the ...
Anie Lusiani +2 more
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Star-path bipartite Ramsey numbers
Discrete Mathematics, 1998 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hattingh, Johannes H. +1 more
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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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Zero-sum bipartite Ramsey numbers [PDF]
Czechoslovak Mathematical Journal, 1993 Let \(G\) be a bipartite graph and let \(k\) be a positive integer which divides the cardinality of the edge set of \(G\), \(E(G)\). The zero-sum bipartite Ramsey number \(B(G,\mathbb{Z}_ k)\) is defined to be the smallest positive integer \(t\) so that, for any \(\mathbb{Z}_ k\)-coloring of the complete bipartite graph \(K_{t,t}\) \((f:E(K_{t,t}) \to \
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Another view of Bipartite Ramsey numbers
, 2022 For bipartite graphs $G$ and $H$ and a positive integer $m$, the $m$-bipartite Ramsey number $BR_m(G, H)$ of $G$ and $H$ is the smallest integer $n$, such that every red-blue coloring of $K_{m,n}$ results in a red $G$ or a blue $H$. Zhenming Bi, Gary Chartrand and Ping Zhang in \cite{bi2018another} evaluate this numbers for all positive integers $m ...
Rowshan, Yaser, Gholami, Mostafa
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