English

Extremal results for random discrete structures

Combinatorics 2016-09-20 v2

Abstract

We study thresholds for extremal properties of random discrete structures. We determine the threshold for Szemer\'edi's theorem on arithmetic progressions in random subsets of the integers and its multidimensional extensions and we determine the threshold for Tur\'an-type problems for random graphs and hypergraphs. In particular, we verify a conjecture of Kohayakawa, \L uczak, and R\"odl for Tur\'an-type problems in random graphs. Similar results were obtained by Conlon and Gowers.

Keywords

Cite

@article{arxiv.1603.00894,
  title  = {Extremal results for random discrete structures},
  author = {Mathias Schacht},
  journal= {arXiv preprint arXiv:1603.00894},
  year   = {2016}
}

Comments

32 pages

R2 v1 2026-06-22T13:02:36.817Z