On the diameter of matroid ports
type: Item
instance of: scholarly article
title: On the diameter of matroid ports
zbMATH Open document ID: 1159.94007
author: Jaume Martí-Farré
author: Carles Padró
author: Leonor Vázquez
published in: The Electronic Journal of Combinatorics
publication date: 2009-04-07T00:00:00Z
full work available at URL: https://eudml.org/doc/129804
full work available at URL: v15i1n27.html
review text: 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.
Mathematics Subject Classification ID: 94A62
Mathematics Subject Classification ID: 52B40
zbMATH DE Number: 5540889
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5540889