a note on the union-closed sets conjecture

Ian Roberts, Jamie Simpson

    Research output: Contribution to journalArticle

    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 languageEnglish
    Pages (from-to)265-267
    Number of pages3
    JournalAustralasian Journal of Combinatorics
    Volume47
    Publication statusPublished - Jun 2010

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