Abstract :
We consider the following model Hr(n, p) of random r-uniform hypergraphs. The vertex set consists of two disjoint subsets V of size | V | = n and U of size | U | = (r − 1)n. Each r-subset of V × (r−1U) is chosen to be an edge of H ϵ Hr(n, p) with probability p = p(n), all choices being independent. It is shown that for every 0 < ε < 1 if p = (C ln n)/nr−1 with C = C(ε) sufficiently large, then almost surely every subset V1 ⊂ V of size | V1 | = ⌊(1 − ε)n⌋ is matchable, that is, there exists a matching M in H such that every vertex of V1 is contained in some edge of M.
