Haoran Luo

On the minimum size of maximal $k$-wise intersecting families

A family $\mathcal{F}$ of subsets of $[n] := \{1,2,\ldots, n\}$ is called maximal $k$-wise intersecting if every collection of at most $k$ members of $\mathcal{F}$ has a non-empty intersection, and adding any other set to $\mathcal{F}$ breaks this property. An old question by Erd\H{o}s and Kleitman from 1974 asks for t...