On interval clutters
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 Tucker's 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 Tucker's result in, many situations. As a lemma, we also determine all the minor minimal clutters that have a circuit subhypcrgraph but not a circuit minor. © 2002 Published by Elsevier Science B.V.
Publication Source (Journal or Book title)
Ding, G. (2002). On interval clutters. Discrete Mathematics, 254 (1-3), 89-102. https://doi.org/10.1016/S0012-365X(01)00354-5