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A note on the union-closed sets conjecture

Roberts, Ian T. and Simpson, Jamie (2010). A note on the union-closed sets conjecture. Australasian Journal of Combinatorics,47:265-267.

Document type: Journal Article
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IRMA ID 81704288xPUB275
Title A note on the union-closed sets conjecture
Author Roberts, Ian T.
Simpson, Jamie
Journal Name Australasian Journal of Combinatorics
Publication Date 2010
Volume Number 47
ISSN 1034-4942   (check CDU catalogue open catalogue search in new window)
Scopus ID 2-s2.0-77953144696
Start Page 265
End Page 267
Total Pages 3
Place of Publication Australia
Publisher Centre for Discrete Mathematics & Computing
HERDC Category C1 - Journal Article (DIISR)
Abstract A collection A of finite sets is closed under union if A, B ∈ A implies that A ∪ B ∈ A. The Union-Closed Sets Conjecture states that if A is a union-closed collection of sets, containing at least one non-empty set, then there is an
element which belongs to at least half of the sets in A. We show that if q is the minimum cardinality of ∪A taken over all
counterexamples A, then any counterexample A has cardinality at least 4q − 1.
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