Claims

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2003_11_01_alon_krivelevich_sudakov: Theorem 5.2 of Alon, Krivelevich and Sudakov (Combin. Probab. Comput. 2003): every bipartite graph with m edges and no isolated vertices has Ramsey number at most 2 to the power 16 root m plus 1.

2010_01_30_sudakov: Sudakov's Theorem 1.1 (Adv. Math. 2011): every graph with m edges and no isolated vertices has Ramsey number at most 2 to the power 250 times the square root of m, which answers the question yes with an explicit constant.

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