On Randomly Generated Non-Trivially Intersecting Hypergraphs

Abstract

We propose two procedures to choose members of ${[n] \choose r}$ sequentially at random to form a non-trivially intersecting hypergraph. In both cases we show what is the limiting probability that if $r=c_nn^{1/3}$ with $c_n \rightarrow c$, then the process results in a Hilton-Milner-type hypergraph.