Ramsey properties of random discrete structures



We study thresholds for Ramsey properties of random discrete structures. In particular, we determine the threshold for Rado's theorem for solutions of partition regular systems of equations in random subsets of the integers and we prove the 1-statement of the conjectured threshold for Ramsey's theorem for random hypergraphs. Those results were conjectured by Rödl and Ruciński and similar results were obtained independently by Conlon and Gowers. © 2010 Wiley Periodicals, Inc. Random Struct. Alg., 2010