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{\bf Jaume Mart\'{\i}-Farr\'e, Carles Padr\'{o} and Leonor V\'{a}zquez}
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{\bf On the Diameter of Matroid Ports}
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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. Brickell and Davenport proved in 1989
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.
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