TY - JOUR

T1 - Almost perfect matchings in random uniform hypergraphs

AU - Krivelevich, Michael

PY - 1997/6/10

Y1 - 1997/6/10

N2 - 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 × (Ur-1) is chosen to be an edge of H ∈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.

AB - 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 × (Ur-1) is chosen to be an edge of H ∈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.

UR - http://www.scopus.com/inward/record.url?scp=0042630949&partnerID=8YFLogxK

U2 - 10.1016/S0012-365X(96)00310-X

DO - 10.1016/S0012-365X(96)00310-X

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AN - SCOPUS:0042630949

SN - 0012-365X

VL - 170

SP - 259

EP - 263

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 1-3

ER -