Co-degrees Resilience for Perfect Matchings in Random Hypergraphs - Ferber, Asaf; Hirschfeld, Lior (The Electronic Journal of Combinatorics, 2020)
In this paper we prove an optimal co-degrees resilience property for the binomial k-uniform hypergraph model H_n,p^k with respect to perfect matchings. That is, for a sufficiently large n which is divisible by k, and p≥ C_kn/n, we prove that with high probability every subgraph HH^k_n,p with minimum co-degree (meaning, the number of supersets every set of size k-1 is contained in) at least (1/2+o(1))np contains a perfect matching.