Hypergraph Packing and Sparse Bipartite Ramsey Numbers

DAVID CONLON
2009 Combinatorics, probability & computing  
We prove that there exists a constant c such that, for any integer ∆, the Ramsey number of a bipartite graph on n vertices with maximum degree ∆ is less than 2 c∆ n. A probabilistic argument due to Graham, Rödl and Ruciński implies that this result is essentially sharp, up to the constant c in the exponent. Our proof hinges upon a quantitative form of a hypergraph packing result of Rödl, Ruciński and Taraz.
doi:10.1017/s0963548309990174 fatcat:eufjgpnn4ve73eiq2dgc7l5rey