$d$-Galvin families

Johan Håstad, Guillaume Lagarde, Joseph Swernofsky

The Galvin problem asks for the minimum size of a family $\mathcal{F}\subseteq \left(\genfrac{}{}{0ex}{}{[n]}{n/2}\right)$ with the property that, for any set $A$ of size $\frac{n}{2}$, there is a set $S \in…