A note on supersaturated set systems. (January 2016)

• Record Type: Journal Article
• Authors: Frankl, Peter; Kohayakawa, Yoshiharu; Rödl, Vojtěch
• Is Part Of: European journal of combinatorics. Volume 51(2016:Jan.)
• Page Start: 190
• Page End: 199
• Publication Date: 2016-01
• Subjects: Combinatorial analysis -- Periodicals; Analyse combinatoire -- Périodiques; Combinatorial analysis; Periodicals; Electronic journals; 511.6
• DOI: 10.1016/j.ejc.2015.03.028
• Languages: English
• ISSNs: 0195-6698

Abstract

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 .