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On the number of maximal intersecting k-uniform families and further applications of Tuza's set pair method
We study the function which denotes the number of maximal
-uniform intersecting families . Improving a
bound of Balogh at al. on , we determine the order of magnitude of
by proving that for any fixed , 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.Comment: 11 page