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On a Conjecture of Frankl and Füredi

By Ameera Chowdhury


Frankl and Füredi conjectured that if F ⊂ 2X is a non-trivial λ-intersecting family of size m, then the number of pairs {x,y} ∈ ( X) 2 that are contained in some F ∈ F is at least ( m) 2 [P. Frankl and Z. Füredi. A Sharpening of Fisher’s Inequality. Discrete Math., 90(1):103-107, 1991]. We verify this conjecture in some special cases, focusing especially on the case where F is additionally required to be k-uniform and λ is small.

Year: 2013
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