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 .