Packing perfect matchings in random hypergraphs

We introduce a new procedure for generating the binomial random graph/hypergraph models, referred to as online sprinkling . As an illustrative application of this method, we show that for any fixed integer k ≥ 3 , the binomial k ‐uniform random hypergraphH n , p kcontains N : = ( 1 − o ( 1 ) ) (n − 1k − 1) p edge‐disjoint perfect matchings, provided p ≥log ⁡ C nn k − 1, where C : = C ( k ) is an integer depending only on k . Our result for N is asymptotically optimal and for p is optimal up to the p o l y l o g ( n ) factor. This significantly improves a result of Frieze and Krivelevich.