### 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.

Original language | English |
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Pages (from-to) | 265-267 |

Number of pages | 3 |

Journal | Australasian Journal of Combinatorics |

Volume | 47 |

Publication status | Published - Jun 2010 |

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## Cite this

Roberts, I., & Simpson, J. (2010). a note on the union-closed sets conjecture.

*Australasian Journal of Combinatorics*,*47*, 265-267.