On matroids of branch-width three.
type: Item
instance of: scholarly article
title: On matroids of branch-width three.
zbMATH Open document ID: 1034.05011
author: Rhiannon Hall
author: Charles Semple
author: James Oxley
author: Geoff Whittle
published in: Journal of Combinatorial Theory. Series B
publication date: 2002-12-10T00:00:00Z
review text: Gian-Carlo Rota conjectured that the set of excluded minors for the class of matroids (combinatorial geometries) that are representable over a fixed finite field is finite [Actes Congr. internat. Math. 1970, 3, 229--233 (1971; Zbl 0362.05044)]. Some partial results are known. For all positive integers \(k\), the class \(\mathcal{B}_k\) of matroids of branch-width at most \(k\) is minor-closed. The first interesting class is \(\mathcal{B}_3\), containing infinite antichains of matroids and is thus not well-quasi-ordered under the minor order. In this paper the authors prove Rota'conjecture for \(\mathcal{B}_3\) (in the cases \(\mathcal{B}_1\) and \(\mathcal{B}_2\) the conjecture is trivial).
reviewed by: Raul Cordovil
Mathematics Subject Classification ID: 05B35
zbMATH DE Number: 1843849
zbMATH Keywords: matroid
zbMATH Keywords: minors
zbMATH Keywords: Rota conjecture
Wikidata QID: Q30054572
MaRDI profile type: Publication
full work available at URL: jctb.2002.2120
OpenAlex ID: W1987279762
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DBLP publication ID: journals/jct/HallOSW02
DOI: 10.1006/JCTB.2002.2120
description: scientific article; zbMATH DE number 1843849