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Hypergraphs with independent neighborhoods

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journal contribution
posted on 22.06.2009 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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Publisher Statement

The final publication is available at Springer via http://dx.doi.org/10.1007/s00493-010-2474-6

Date

22/06/2009

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