Claims

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2008_03_24_johansson_kahn_vu: Johansson, Kahn and Vu prove that the threshold for a perfect matching in a random 3-uniform hypergraph on 3n vertices is of order n log n, settling Shamir's problem up to the constant; refereed in 2008 and credited.

2019_09_15_kahn: Kahn proves that a random r-uniform hypergraph on N vertices with more than (1+epsilon)(N/r) log N edges almost surely has a perfect matching, so the threshold for the problem is asymptotic to n log n; refereed in 2023.

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