%0 Journal Article
%T On the number of maximal intersecting k-uniform families and further applications of Tuza's set pair method
%A Zolt¨˘n L¨®r¨˘nt Nagy
%A Bal¨˘zs Patk¨®s
%J Mathematics
%D 2015
%I arXiv
%X We study the function $M(n,k)$ which denotes the number of maximal $k$-uniform intersecting families $F\subseteq \binom{[n]}{k}$. Improving a bound of Balogh at al. on $M(n,k)$, we determine the order of magnitude of $\log M(n,k)$ by proving that for any fixed $k$, $M(n,k) =n^{\Theta(\binom{2k}{k})}$ holds. Our proof is based on Tuza's set pair approach. The main idea is to bound the size of the largest possible point set of a cross-intersecting system. We also introduce and investigate some related functions and parameters.
%U http://arxiv.org/abs/1501.00648v2