A note on supersaturated set systems

Frankl, Péter and Kohayakawa, Y. and Rödl, V. (2016) A note on supersaturated set systems. EUROPEAN JOURNAL OF COMBINATORICS, 51. pp. 190-199. ISSN 0195-6698

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Abstract

A well-known theorem of Erdos, Ko and Rado implies that any family ℱ of k-element subsets of an n-element set with more than n-tk-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|=αn-tk-t and α>1. © 2015 Elsevier Ltd.

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