Infinite Gammoids

Finite strict gammoids, introduced in the early 1970's, are matroids defined via finite digraphs equipped with some set of sinks: a set of vertices is independent if it admits a linkage to these sinks. In particular, an independent set is maximal (i.e. a base) precisely if it is linkable onto t...

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Bibliographic Details
Published in:The Electronic journal of combinatorics 2015-03, Vol.22 (1)
Main Authors: Afzali Borujeni, Seyed Hadi, Law, Hiu-Fai, Müller, Malte
Format: Article
Language:English
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Summary:Finite strict gammoids, introduced in the early 1970's, are matroids defined via finite digraphs equipped with some set of sinks: a set of vertices is independent if it admits a linkage to these sinks. In particular, an independent set is maximal (i.e. a base) precisely if it is linkable onto the sinks.In the infinite setting, this characterization of the maximal independent sets need not hold. We identify a type of substructure as the unique obstruction. This allows us to prove that the sets linkable onto the sinks form the bases of a (possibly non-finitary) matroid if and only if this substructure does not occur.
ISSN:1077-8926
1077-8926
DOI:10.37236/4181