On interval clutters Original Research Article

A hypergraph is an interval hypergraph if its vertices can be linearly ordered so that all its edges are consecutive sets. Interval hypergraphs have been characterized by Tucker (J. Combin. Theory 12 (1972) 153) in terms of excluded subhypergraphs. In this paper, we strengthen Tuckerʹs result for clutters by characterizing interval clutters in terms of excluded partial clutters, as well as excluded minors. Since minor and partial clutter relations are much more restrictive than the subhypergraph relation, our results are more applicable than Tuckerʹs result in many situations. As a lemma, we also determine all the minor minimal clutters that have a circuit subhypergraph but not a circuit minor.