Geodesic
Another View of Bipartite Ramsey Numbers
Discussiones Mathematicae. Graph Theory, Tome 38 (2018) no. 2, pp. 587-605

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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. We evaluate this number for all positive integers s when F = K2,2 and H ∈ K2,3,K3,3.
Keywords: Ramsey number, bipartite Ramsey number, s -bipartite Ramsey number 
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Bi, Zhenming; Chartrand, Gary; Zhang, Ping. Another View of Bipartite Ramsey Numbers. Discussiones Mathematicae. Graph Theory, Tome 38 (2018) no. 2, pp. 587-605. http://geodesic.mathdoc.fr/item/DMGT_2018_38_2_a17/