On Families of Weakly Cross-intersecting Set-pairs

Abstract

Let ℱ be a family of pairs of sets. We call it an (a, b)-set system if for every set-pair (A,B) in ℱ we have that |A| = a, |B| = b, and A ∩ B = Ø. Furthermore, ℱ is weakly cross-intersecting if for any (Ai , Bi ), (Aj , Bj ) ∈ ℱ with i ≠ j we have th