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Completion and decomposition of a clutter into representable matroids

Author

Martí Farré, Jaume

Mier Vinué, Anna de

Other authors

Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV

Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada II

Universitat Politècnica de Catalunya. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions

Universitat Politècnica de Catalunya. MD - Matemàtica Discreta

Publication date

2015-05-01

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Abstract

This paper deals with the question of completing a monotone increasing family of subsets Gamma of a finite set Omega to obtain the linearly dependent subsets of a family of vectors of a vector space. Specifically, we prove that such vectorial completions of the family of subsets Gamma exist and, in addition, we show that the minimal vectorial completions of the family Gamma provide a decomposition of the clutter Lambda of the inclusion-minimal elements of Gamma. The computation of such vectorial decomposition of clutters is also discussed in some cases. (C) 2015 Elsevier Inc. All rights reserved.

Peer Reviewed

Postprint (author’s final draft)

Document Type

Article

Language

English

Subjects and keywords

Àrees temàtiques de la UPC::Matemàtiques i estadística::Probabilitat; Graph theory; Clutter; Hypergraph; Matroid; Decomposition; Representable matroid; Teoria de grafs; Classificació AMS::05 Combinatorics::05C Graph theory

Publisher

Elsevier

Related items

http://www.sciencedirect.com/science/article/pii/S002437951500052X

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DIDL MARC MARC_CCUC METS OAI_DC ORE QDC RDF

Rights

http://creativecommons.org/licenses/by-nc-nd/3.0/es/

Open Access

This item appears in the following Collection(s)

E-prints [72986]