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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, Edy Tri Baskoro, Suhadi Wido Saputro   +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., Henning, Michael A.   +1 more
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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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The history of degenerate (bipartite) extremal graph problems [PDF]

, 2013
This paper is a survey on Extremal Graph Theory, primarily focusing on the case when one of the excluded graphs is bipartite. On one hand we give an introduction to this field and also describe many important results, methods, problems, and constructions.
A. A. Razborov, A. F. Sidorenko, A. F. Sidorenko, A. G. Thomason, A. Grzesik, A. Gyárfás, A. Gyárfás, A. Gyárfás, A. Kostochka, A. Lubotzky, A. Marcus, A. McLennan, A. Scott, A. Sidorenko, A. Thomason, B. Bollobás, B. Bollobás, B. Bollobás, B. Bollobás, B. Bollobás, B. Sudakov, B. Toft, C. Balbuena, C. Balbuena, C. Balbuena, C. Hyltén-Cavallius, C. Jagger, C. R. J. Clapham, C. T. Benson, D. Bienstock, D. Caen de, D. Conlon, D. K. Garnick, D. K. Garnick, D. Kühn, D. M. Cvetkovič, D. Mubayi, D. Piguet, D. R. Woodall, D. R. Woodall, E. Győri, E. Győri, E. Győri, E. Szemerédi, F. Behrend, F. Chung, F. Lazebnik, F. Lazebnik, F. Lazebnik, F. Lazebnik, F. Lazebnik, F. Lazebnik, F. R. K. Chung, G. A. Margulis, G. A. Margulis, G. A. Margulis, G. Fan, G. Fan, G. Megyesi, G. N. Kopylov, G. N. Sárközy, G. Tardos, Gy. Katona, H. Edelsbrunner, H. Hatami, H. Hatami, H. Hatami, I. Reiman, I. Reiman, J. A. Bondy, J. A. Bondy, J. A. Bondy, J. Beck, J. Fox, J. Griggs, J. Kollár, J. Komlós, J. Komlós, J. Pach, J. R. Griggs, J. R. Griggs, J. Shen, J. Spencer, J. Verstraëte, J.-F. Saclè, K. Clarkson, K. Zarankiewicz, K. Čulík, L. Babai, L. Caccetta, L. Lovász, L. Lovász, M. Conder, M. Klazar, M. Molloy, M. Mörs, M. N. Huxley, M. Simonovits, M. Simonovits, M. Simonovits, M. Simonovits, M. Simonovits, M. Simonovits, M. Simonovits, M. Woźniak, N. Alon, N. Alon, N. Alon, N. Alon, N. Alon, O. Cooley, O. Pikhurko, P. Brass, P. Erdős, P. Erdős, P. Erdős, P. Erdős, P. Erdős, P. Erdős, P. Erdős, P. Erdős, P. Erdős, P. Erdős, P. Erdős, P. Erdős, P. Erdős, P. Erdős, P. Erdős, P. Erdős, P. Erdős, P. Erdős, P. Erdős, P. Erdős, P. Erdős, P. Erdős, P. Erdős, P. Erdős, P. Erdős, P. Erdős, P. Erdős, P. Erdős, P. Erdős, P. Keevash, P. N. Balister, P. N. Balister, P. Turán, P. Turán, P. Turán, P. Turán, R. Baer, R. Canham, R. J. Faudree, R. J. Faudree, R. K. Guy, R. K. Guy, R. M. Wilson, R. Pinchasi, R. R. Singleton, R. Wenger, S. Ball, S. Brandt, S. Hartman, S. Janson, S. Józsa, T. Jiang, T. Jiang, T. Kővári, V. Nikiforov, V. Nikiforov, W. G. Brown, W. G. Brown, W. G. Brown, W. G. Brown, W. G. Brown, W. G. Brown, W. Imrich, W. Mader, W. Mader, W. Mader, Y. Yuansheng, Y. Yuansheng, Z. Füredi, Z. Füredi, Z. Füredi, Z. Füredi, Z. Füredi, Z. Füredi, Z. Füredi, Z. Füredi, Z. Füredi, Z. Füredi, Z. Füredi, Z. Füredi, Z. Füredi, Z. Füredi, Z. Füredi, Z. Füredi, Znám, Znám   +198 more
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Cycles are strongly Ramsey-unsaturated

, 2012
We call a graph H Ramsey-unsaturated if there is an edge in the complement of H such that the Ramsey number r(H) of H does not change upon adding it to H.
Burr, J. SKOKAN, Komlós, M. STEIN, Szemerédi   +4 more
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An approximate version of Sidorenko's conjecture [PDF]

, 2010
A beautiful conjecture of Erd\H{o}s-Simonovits and Sidorenko states that if H is a bipartite graph, then the random graph with edge density p has in expectation asymptotically the minimum number of copies of H over all graphs of the same order and edge ...
Conlon, David, Fox, Jacob, Sudakov, Benny   +2 more
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On Generalizations of Pairwise Compatibility Graphs [PDF]

Discrete Mathematics & Theoretical Computer Science
A graph $G$ is a pairwise compatibility graph (PCG) if there exists an edge-weighted tree and an interval $I$, such that each leaf of the tree is a vertex of the graph, and there is an edge $\{ x, y \}$ in $G$ if and only if the weight of the path in the
Tiziana Calamoneri, Manuel Lafond, Angelo Monti, Blerina Sinaimeri   +3 more
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Multicolor Ramsey Numbers For Complete Bipartite Versus Complete Graphs [PDF]

Journal of Graph Theory, 2013
AbstractLet be graphs. The multicolor Ramsey number is the minimum integer r such that in every edge‐coloring of by k colors, there is a monochromatic copy of in color i for some . In this paper, we investigate the multicolor Ramsey number , determining the asymptotic behavior up to a polylogarithmic factor for almost all ranges of t and m. Several
Lenz, John, Mubayi, Dhruv
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