# FC-families and improved bounds for Frankl's conjecture

@article{Morris2006FCfamiliesAI, title={FC-families and improved bounds for Frankl's conjecture}, author={R. Morris}, journal={Eur. J. Comb.}, year={2006}, volume={27}, pages={269-282} }

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… Expand

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#### 29 Citations

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