FC-families and improved bounds for Frankl's conjecture

@article{Morris2006FCfamiliesAI,
  title={FC-families and improved bounds for Frankl's conjecture},
  author={Robert 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… CONTINUE READING

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