Feb 13, 2007 · 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 ...
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, ...
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, ...
Frankl's conjecture states that in a family of sets closed by union F such that F 6= {∅}, there is an element that belongs to at least half of the sets of ...
Feb 13, 2007 · FC-FAMILIES AND FRANKL'S CONJECTURE. 3 on union-closed families with many 2-sets, and discuss the asymptotics of FC(k, n) as n → с. In this ...
Improved Lower Bound for Frankl's Union-Closed Sets Conjecture
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Sep 20, 2024 · We verify an explicit inequality conjectured in [Gilmer, 2022, arXiv:2211.09055], thus proving that for any nonempty union-closed family F ...
FC-families are families for which it is proved that every union-closed family containing them satisfies the Frankl's condition (e.g., in every union-closed ...
The union-closed sets conjecture, also known as Frankl's conjecture, is an open problem in combinatorics posed by Péter Frankl in 1979.
FC-families and improved bounds for Frankl's conjecture. Overview of attention for article published in European Journal of Combinatorics, February 2006.
Nov 30, 2011 · [15] R. Morris, FC-families and improved bounds for Frankl's conjecture, Eu- ropean J. Combin. 27 (2006), 269–282.