A note on supersaturated set systems. (January 2016) - Frankl, Peter; Kohayakawa, Yoshiharu; Rödl, Vojtěch
Abstract: A well-known theorem of Erdős, Ko and Rado implies that any family ℱ of k -element subsets of an n -element set with more than n − t k − t members must contain two members F and F ′ with | F ∩ F ′ | < t, as long as n is sufficiently large with respect to k and t . We investigate how many such pairs ( F, F ′ ) ∈ ℱ × ℱ there must be in any such family ℱ with | ℱ | = α n − t k − t and α > 1 .