On randomly generated intersecting hypergraphs

Abstract

Let $c$ be a positive constant. We show that if $r=\lfloor c{n}^{1/3}\rfloor$ and the members of $\left(\genfrac{}{}{0ex}{}{[n]}{r}\right)$ are chosen sequentially at random to form an intersecting hypergraph then with limiting probability $(1+c^3{)}^{-1}$, as $n\to \infty$, the resulting family will be of maximum size $\left(\genfrac{}{}{0ex}{}{n-1}{r-1}\right)$.

10 pages in Electron. J. Combin. 10 (2003), Research Paper 29, 10pp