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- W3167180680 abstract "A family F has covering number τ if the size of the smallest set intersecting all sets from F is equal to τ. Let M(n,k,τ) stand for the size of the largest intersecting family F of k-element subsets of {1,…,n} with covering number τ. It is a classical result of Erdős and Lovász that M(n,k,k)≤kk for any n. In this short note, we explore the behavior of M(n,k,τ) for n<k2 and large τ. The results are quite surprising: For example, we show that M(n,k,τ)=(1−o(1))n−1k−1,if n=⌊k3/2⌋ and τ≤k−k3/4+o(1) as k→∞<e−ck1/2nk,if n=⌊k3/2⌋ and τ>k−12k1/2." @default.
- W3167180680 created "2021-06-22" @default.
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- W3167180680 date "2023-10-01" @default.
- W3167180680 modified "2023-10-17" @default.
- W3167180680 title "Uniform intersecting families with large covering number" @default.
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- W3167180680 doi "https://doi.org/10.1016/j.ejc.2023.103747" @default.
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