Hypergraphs with independent neighborhoods

For each k ≥ 2, let ρk ∈ (0, 1) be the largest number such that there exist k-uniform hypergraphs on n vertices with independent neighborhoods and (ρk + o(1))(kn) edges as n → ∞. We prove that ρk = 1 − 2logk/k + Θ(log log k/k) as k → ∞. This disproves a conjecture of Füredi and the last two authors.

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