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Completion and decomposition of a clutter into representable matroids

Author
Martí-Farré, J.; De Mier, A.
Type of activity
Journal article
Journal
Linear algebra and its applications
Date of publication
2015-05-01
Volume
472
First page
31
Last page
47
DOI
https://doi.org/10.1016/j.laa.2015.01.023 Open in new window
Project funding
Combinatoria, teoría de grafos y geometría discreta
Optimización y problemas extremales en teoria de grafos y combinatoria. Aplicacions a les redes de comunicación
Repository
http://hdl.handle.net/2117/78129 Open in new window
URL
http://www.sciencedirect.com/science/article/pii/S002437951500052X Open in new window
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...
Citation
Martí-Farré, J., De Mier, A. Completion and decomposition of a clutter into representable matroids. "Linear algebra and its applications", 01 Maig 2015, vol. 472, p. 31-47.
Keywords
Clutter, Decomposition, Hypergraph, Matroid, Representable matroid
Group of research
COMBGRAPH - Combinatorics, Graph Theory and Applications
GAPCOMB - Geometric, Algebraic and Probabilistic Combinatorics

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