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

Abstract

We study the function M(n, k) which denotes the number of maximal k-uniform intersecting families F ⊆ (Formula presented). Improving a bound of Balogh, Das, Delcourt, Liu and Sharifzadeh on M(n; k), we determine the order of magnitude of logM(n, k) by proving that for any fixed k, M(n, k) = nΘ (Formula presented) 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.