On the maximum number of points in a maximal intersecting family of finite sets

Majumder, Kaushik

doi:10.48550/arxiv.1402.7158

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Proposition 23 For Any Positive Integers K and N We Have1

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2015

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“…Note that such a family is unextendable not only by any k-subsets of its underlying set, but by any k-sets in the universe at all. This kind of maximal intersecting set systems were studied a lot, the best known upper bound on f (k) is due to Majumder [16], stating that f (k)…”

Section: Proposition 23 For Any Positive Integers K and N We Havementioning

confidence: 99%

On the Number of Maximal Intersecting $k$-Uniform Families and Further Applications of Tuza's Set Pair Method

Nagy

Patkós

2015

Electron. J. Combin.

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We study the function M (n, k) which denotes the number of maximal k-uniform intersecting families F ⊆ [n] k . Improving a bound of Balogh, Das, Delcourt, Liu and Sharifzadeh 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(( 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 crossintersecting system. We also introduce and investigate some related functions and parameters.

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Section: Proposition 23 For Any Positive Integers K and N We Havementioning

confidence: 99%