Almost perfect matchings in random uniform hypergraphs

Michael Krivelevich*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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 × (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.

Original languageEnglish
Pages (from-to)259-263
Number of pages5
JournalDiscrete Mathematics
Volume170
Issue number1-3
DOIs
StatePublished - 10 Jun 1997

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