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arXiv · 1605.07607

On randomly generated intersecting hypergraphs II

Tom Bohman·Alan Frieze·Ryan R. Martin·Miklós Ruszinkó·Cliff Smyth
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Abstract

Let $c$ be a positive constant. Suppose that $r=o(n^{5/12})$ and the members of $\binom{[n]}{r}$ are chosen sequentially at random to form an intersecting hypergraph $\mathcal{H}$. We show that whp $\mathcal{H}$ consists of a simple hypergraph $\mathcal{S}$ of size $\Theta(r/n^{1/3})$, a distinguished vertex $v$ and all $r$-sets which contain $v$ and meet every edge of $\mathcal{S}$. This is a continuation of the study of such random intersecting systems started in [Electron. J. Combin, (2003) R29] where the case $r=O(n^{1/3})$ was considered. To obtain the stated result we continue to investigate this question in the range $\omega(n^{1/3})\le r \le o(n^{5/12})$.

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Tom Bohman, Alan Frieze, Ryan R. Martin, Miklós Ruszinkó, Cliff Smyth. 2016-05-23. On randomly generated intersecting hypergraphs II. https://doi.org/10.1002/rsa.20152

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