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Families Implying the Frankl Conjecture

Authors
Journal
European Journal of Combinatorics
0195-6698
Publisher
Elsevier
Publication Date
Volume
23
Issue
7
Identifiers
DOI: 10.1006/eujc.2002.0586

Abstract

Abstract A union closed (UC) family A is a finite family of sets such that the union of any two sets in A is also in A. Peter Frankl conjectured that for every union closed family A, there exists some x contained in at least half the members of A. An FC-family is a UC family B such that for every UC family A, if B ⊆ A, then A satisfies the Frankl conjecture. We construct several such families, involving five, six, and seven elements.

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