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arXiv · 1501.00648

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

Zoltán Lóránt Nagy·Balázs Patkós
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Abstract

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 $k$, $M(n,k) =n^{Θ(\binom{2k}{k})}$ 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.

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Zoltán Lóránt Nagy, Balázs Patkós. 2015-03-12. On the number of maximal intersecting k-uniform families and further applications of Tuza's set pair method. https://arxiv.org/abs/1501.00648

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