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Hypergraphs with independent neighborhoods

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journal contribution
posted on 22.06.2009, 00:00 by Tom Bohman, Alan 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.


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