Ben Lund, Maximal 3-wise intersecting families

A family $\mathcal{F}$ of subsets of {1,2,…,n} is called maximal k-wise intersecting if every collection of at most k members from $\mathcal{F}$ has a common element, and moreover, no set can be added to $\mathcal{F}$ while preserving this property. In 1974, Erdős and Kleitman asked for the smallest possible size of a maximal k-wise intersecting family, for k≥3. We resolve this problem for k=3 and n even and sufficiently large.

This is joint work with Kevin Hendrey, Casey Tompkins, and Tuan Tran.