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 R¨odl and Ruci´nski and similar results were obtained independently by Conlon and Gowers.

• Type: Journal
• Year: 2010
• Where: RSA
• Authors: Ehud Friedgut, Vojtech Rödl, Mathias Schacht
• Keywords: Conjectured Threshold, Partition Regular Systems, Random Discrete Structures, RSA 2010