Maximal 3-Wise Intersecting Families
نویسندگان
چکیده
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 has non-empty intersection, and no other can be added to while maintaining this property. In 1974, Erdős Kleitman asked for the minimum size a family. We answer their question $$k=3$$ sufficiently large n. show that unique obtained by partitioning [n] into two B with almost equal sizes taking consisting all proper supersets B.
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ژورنال
عنوان ژورنال: Combinatorica
سال: 2023
ISSN: ['0209-9683', '1439-6912']
DOI: https://doi.org/10.1007/s00493-023-00046-3