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Electronic Journal of Combinatorics
Article . 2008 . Peer-reviewed
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Article . 2008
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Article . 2008
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On the Diameter of Matroid Ports

On the diameter of matroid ports
Authors: Jaume Martí-Farré; Carles Padró; Leonor Vázquez;

On the Diameter of Matroid Ports

Abstract

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.

Related Organizations
Keywords

Matroids in convex geometry (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.), Authentication, digital signatures and secret sharing

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
gold