On Erdős–Ko–Rado for Random Hypergraphs II

  title={On Erdős–Ko–Rado for Random Hypergraphs II},
  author={Arran Hamm and Jeff Kahn},
  journal={Combinatorics, Probability and Computing},
  pages={61 - 80}
  • Arran Hamm, J. Kahn
  • Published 23 June 2014
  • Mathematics
  • Combinatorics, Probability and Computing
Denote by ${\mathcal H}_k$(n, p) the random k-graph in which each k-subset of {1,. . .,n} is present with probability p, independent of other choices. More or less answering a question of Balogh, Bohman and Mubayi, we show: there is a fixed ε > 0 such that if n = 2k + 1 and p > 1 - ε, then w.h.p. (that is, with probability tending to 1 as k → ∞), ${\mathcal H}_k$(n, p) has the ‘Erdős–Ko–Rado property’. We also mention a similar random version of Sperner's theorem. 
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