On the diameter of matroid ports
Summary: A clutter or antichain on a set defines a hypergraph. Matroid ports are a special class of clutters, and this paper deals with the diameter of matroid ports, that is, the diameter of the corresponding hypergraphs. Specifically, we prove that the diameter of every matroid port is at most 2. The main interest of our result is its application to secret sharing. \textit{E. F. Brickell} and \textit{D. M. Davenport} [J. Cryptology 4, No. 2, 123--134 (1991; Zbl 0747.94010)] proved that the minimal qualified subsets of every ideal secret sharing scheme form a matroid port. Therefore, our result provides a new necessary condition for an access structure to admit an ideal secret sharing scheme.
scientific article; zbMATH DE number 5540889