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 - https://www.scopus.com/pages/publications/0042630949
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 -