Erdős–ko–rado in random hypergraphs
Combinatorics, Probability and Computing
On the random satisfiable process
Combinatorics, Probability and Computing
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Let c be a positive constant. Suppose that r =o(n5/12) and the members of $({{[n]}\atopr})$ are chosen sequentially at random to form an intersectinghypergraph ${\cal H}$. We show that whp (A sequence ofevents ${\cal E}_1,\ldots,{\cal E}_n,\ldots$ is said to occurwith high probability (whp)$\lim_{n\to\infty}\Pr({\cal E}_n)=1$.) ${\cal H}$ consists of asimple hypergraph ${\cal S}$ of size˜(r/n1/3), a distinguishedvertex v and all r-sets that contain v andmeet every edge of ${\cal S}$. This is a continuation of the studyof such random intersecting systems started in (Bohman et al.,Electronic J Combinatorics (2003) R29) where the case r =O(n1/3) was considered. To obtain thestated result we continue to investigate this question in the rangeÉ(n1/3) d r do(n5/12). © 2006 Wiley Periodicals,Inc. Random Struct. Alg., 2007