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- W4380484898 abstract "A family $${mathcal {F}}$$ on ground set $$[n]:={1,2,ldots , n}$$ is maximal k-wise intersecting if every collection of at most k sets in $${mathcal {F}}$$ has non-empty intersection, and no other set can be added to $${mathcal {F}}$$ while maintaining this property. In 1974, Erdős and Kleitman asked for the minimum size of a maximal k-wise intersecting family. We answer their question for $$k=3$$ and sufficiently large n. We show that the unique minimum family is obtained by partitioning the ground set [n] into two sets A and B with almost equal sizes and taking the family consisting of all the proper supersets of A and of B." @default.
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- W4380484898 date "2023-06-13" @default.
- W4380484898 modified "2023-09-26" @default.
- W4380484898 title "Maximal 3-Wise Intersecting Families" @default.
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- W4380484898 doi "https://doi.org/10.1007/s00493-023-00046-3" @default.
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