Packing perfect matchings in random hypergraphs
نویسنده
چکیده
We introduce a new procedure for generating the binomial random graph/hypergraph models, referred to as online sprinkling. As an illustrative application of this method, we show that for any fixed integer k ≥ 3, the binomial k-uniform random hypergraph H n,p contains N := (1 − o(1)) ( n−1 k−1 ) p edge-disjoint perfect matchings, provided p ≥ log C n nk−1 , where C := C(k) is an integer depending only on k. Our result for N is asymptotically optimal and for p is optimal up to the polylog(n) factor. This significantly improves a result of Frieze and Krivelevich.
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