A Stronger Version of the Union-closed Sets Conjecture

Zhen Cui, Ze-Chun Hu

Published 2017-11-12Version 1

The union-closed sets conjecture (Frankl's conjecture) says that for any finite union-closed family of finite sets, other than the family consisting only of the empty set, there exists an element that belongs to at least half of the sets in the family. In this paper, we introduce a stronger version of Frankl's conjecture and give a partial proof.