Hypergraphs with independent neighborhoods
journal contributionposted on 2009-06-22, 00:00 authored by Tom Bohman, Alan FriezeAlan Frieze, Dhruv Mubayi, Oleg Pikhurko
For each k ≥ 2, let ρ k ∈ (0, 1) be the largest number such that there exist k-uniform hypergraphs on n vertices with independent neighborhoods and (ρ k + o(1))( k n ) edges as n → ∞. We prove that ρ k = 1 − 2logk/k + Θ(log log k/k) as k → ∞. This disproves a conjecture of Füredi and the last two authors.