J Austral Math Soc Ser A 57 pp230--236, 1994.

A Note on the Union-Closed Sets Conjecture

Giovanni Lo Faro

(Received 10 July 1991; revised 20 January 1992)

Abstract

It has been conjectured that for any union-closed set A there exists some element which is contained in at least half the sets in A. It is shown that this conjecture is true if the number of sets in A is less than 25. Several conditions on a counterexample are also obtained.

1991 AMS Subject Classification: 05A05, 05A99

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Authors

Giovanni Lo Faro: Departimento di Matematica, Universita di Messina, Contrada Papardo--Salita Sperone, 31, 98166 Sant' Agata, Messina, Italy.

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Last Modified: Thu Jan 9 9:04:22 2003