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A note of the union-closed sets conjecture

Part of: Combinatorics

Published online by Cambridge University Press:  09 April 2009

R. M. Norton  and
D. G. Sarvate
R. M. Norton
Affiliation:
College of Charleston, Charleston, SC 29424, USA
D. G. Sarvate
Affiliation:
College of Charleston, Charleston, SC 29424, USA
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Abstract

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Let = {A1, …, An} be a union-closed set. This note establishes a property which must be possessed by any smallest counterexample to the Union-Closed Sets Conjecture. Specifically, a counterexample to the conjecture with minimal n has at least three distinct elements, each of which appears in exactly (n − 1)/2 of the .

MSC classification

Secondary: 05A99: None of the above, but in this section
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 55 , Issue 3 , December 1993 , pp. 411 - 413
Copyright
Copyright © Australian Mathematical Society 1993

References

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