Extremal results for random discrete structures

Abstract

We study thresholds for extremal properties of random discrete structures. We determine the threshold for Szemerédi’s theorem on arithmetic progressions in random subsets of the integers and its multidimensional extensions, and we determine the threshold for Turán-type problems for random graphs and hypergraphs. In particular, we verify a conjecture of Kohayakawa, \L uczak, and Rödl for Turán-type problems in random graphs. Similar results were obtained independently by Conlon and Gowers.

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Authors

Mathias Schacht

Fachbereich Mathematik, Universität Hamburg, Hamburg, Germany