Almost perfect matchings in random uniform hypergraphs |
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Authors: | Michael Krivelevich |
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Affiliation: | Department of Mathematics, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, 69978, Israel |
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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 < < 1 if P = (C ln n)/nr−1 with C = C() sufficiently large, then almost surely every subset V1 V of size | V1 | = (1 − )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. |
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