On the number of maximal intersecting k-uniform families and further applications of Tuza's set pair method

Zoltán Lóránt Nagy, Balázs Patkós

We study the function $M(n,k)$ which denotes the number of maximal $k$-uniform intersecting families $F\subseteq \left(\genfrac{}{}{0ex}{}{[n]}{k}\right)$. Improving a bound of Balogh at al. on $M(n,k)$, we…