Uniform s-Cross-Intersecting Families. (28th March 2017) - FRANKL, PETER; KUPAVSKII, ANDREY
Abstract : In this paper we study a question related to the classical Erdős–Ko–Rado theorem, which states that any family of k -element subsets of the set [ n ] = 1, . . ., n in which any two sets intersect has cardinality at most n-1k-1 . We say that two non-empty families A, B[n]k are s-cross-intersecting if, for any A ∈ A, B ∈ B, we have | A ∩ B | ≥ s . In this paper we determine the maximum of | A |+| B | for all n . This generalizes a result of Hilton and Milner, who determined the maximum of | A |+| B | for non-empty 1-cross-intersecting families.