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- W2022700105 abstract "A family of sets A is said to be union-closed if { A ∪ B : A , B ∈ A } ⊂ A . Frankl’s conjecture states that given any finite union-closed family of sets, not all empty, there exists an element contained in at least half of the sets. Here we prove that the conjecture holds for families containing three 3-subsets of a 5-set, four 3-subsets of a 6-set, or eight 4-subsets of a 6-set, extending work of Poonen and Vaughan. As an application we prove the conjecture in the case that the largest set has at most nine elements, extending a result of Gao and Yu. We also pose several open questions." @default.
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- W2022700105 date "2006-02-01" @default.
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- W2022700105 title "FC-families and improved bounds for Frankl’s conjecture" @default.
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- W2022700105 doi "https://doi.org/10.1016/j.ejc.2004.07.012" @default.
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