Geodesic
From clutters to matroids
Jaume Martí-Farré1
1Universitat Politècnica de Catalunya
The electronic journal of combinatorics, Tome 21 (2014) no. 1
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This paper deals with the question of completing a monotone increasing family of subsets $\Gamma$ of a finite set $\Omega$ to obtain the dependent sets of a matroid. Specifically, we provide several natural processes for transforming the clutter $\Lambda$ of the inclusion-minimal subsets of the family $\Gamma$ into the set of circuits ${\cal C}({\cal M})$ of a matroid ${\cal M}$ with ground set $\Omega$. In addition, by combining these processes, we prove that all the minimal matroidal completions of the family can be obtained.
DOI : 10.37236/3895
Classification : 05B35, 05C65
Mots-clés : clutter, hypergraph, matroid, circuits

Jaume Martí-Farré  1

1 Universitat Politècnica de Catalunya 
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     title = {From clutters to matroids},
     journal = {The electronic journal of combinatorics},
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Jaume Martí-Farré. From clutters to matroids. The electronic journal of combinatorics, Tome 21 (2014) no. 1. doi: 10.37236/3895

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