Transformation and decomposition of clutters into matroids
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| Název: | Transformation and decomposition of clutters into matroids |
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| Autoři: | Universitat Politècnica de Catalunya. Departament de Matemàtiques, Universitat Politècnica de Catalunya. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions, Universitat Politècnica de Catalunya. MD - Matemàtica Discreta, Martí Farré, Jaume, Mier Vinué, Anna de |
| Informace o vydavateli: | 2017-05-25 |
| Druh dokumentu: | Electronic Resource |
| Abstrakt: | A clutter is a family of mutually incomparable sets. The set of circuits of a matroid, its set of bases, and its set of hyperplanes are examples of clutters arising from matroids. In this paper we address the question of determining which are the matroidal clutters that best approximate an arbitrary clutter ¿. For this, we first define two orders under which to compare clutters, which give a total of four possibilities for approximating ¿ (i.e., above or below with respect to each order); in fact, we actually consider the problem of approximating ¿ with clutters from any collection of clutters S, not necessarily arising from matroids. We show that, under some mild conditions, there is a finite non-empty set of clutters from S that are the closest to ¿ and, moreover, that ¿ is uniquely determined by them, in the sense that it can be recovered using a suitable clutter operation. We then particularize these results to the case where S is a collection of matroidal clutters and give algorithmic procedures to compute these clutters. Peer Reviewed Postprint (author's final draft) |
| Témata: | Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria, Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs, Combinatorial analysis, Graph theory, Clutter, Matroid, Decomposition, Poset, Combinatòria, Teoria de grafs, Classificació AMS::05 Combinatorics::05B Designs and configurations, Classificació AMS::05 Combinatorics::05C Graph theory, Article |
| URL: | |
| Dostupnost: | Open access content. Open access content Open Access |
| Poznámka: | 29 p. application/pdf English |
| Other Numbers: | HGF oai:upcommons.upc.edu:2117/112728 Martí-Farré, J., De Mier, A. Transformation and decomposition of clutters into matroids. "Advances in mathematics", 25 Maig 2017, vol. 312, p. 286-314. 0001-8708 10.1016/j.aim.2017.03.022 1020267907 |
| Přispívající zdroj: | UNIV POLITECNICA DE CATALUNYA From OAIster®, provided by the OCLC Cooperative. |
| Přístupové číslo: | edsoai.on1020267907 |
| Databáze: | OAIster |
Nájsť tento článok vo Web of Science | Abstrakt: | A clutter is a family of mutually incomparable sets. The set of circuits of a matroid, its set of bases, and its set of hyperplanes are examples of clutters arising from matroids. In this paper we address the question of determining which are the matroidal clutters that best approximate an arbitrary clutter ¿. For this, we first define two orders under which to compare clutters, which give a total of four possibilities for approximating ¿ (i.e., above or below with respect to each order); in fact, we actually consider the problem of approximating ¿ with clutters from any collection of clutters S, not necessarily arising from matroids. We show that, under some mild conditions, there is a finite non-empty set of clutters from S that are the closest to ¿ and, moreover, that ¿ is uniquely determined by them, in the sense that it can be recovered using a suitable clutter operation. We then particularize these results to the case where S is a collection of matroidal clutters and give algorithmic procedures to compute these clutters.<br />Peer Reviewed<br />Postprint (author's final draft) |
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