Disjoint cocircuits in matroids with large rank
type: Item
instance of: scholarly article
title: Disjoint cocircuits in matroids with large rank
zbMATH Open document ID: 1032.05028
DOI: 10.1016/S0095-8956(02)00010-2
author: A. M. H. Gerards
author: James F. Geelen
author: Geoff Whittle
published in: Journal of Combinatorial Theory. Series B
publication date: 2003-08-25T00:00:00Z
review text: To gain insight into minor-closed classes of GF\((q)\)-representable matroids that omit a given characteristic, the authors prove the following theorem: For any positive integers \(n, k\), and \(q\), there exists an integer \(R\) such that, if \(M\) is a matroid with no \(M(K_n)\)- or \(U_{2, q+2}\)-minor, then either \(M\) has a collection of \(k\) disjoint cocircuits or \(M\) has rank at most \(R\). Applied to the class of cographic matroids, this result implies the edge-disjoint version of the Erdős-Pósa theorem [see \textit{P. Erdős} and \textit{L. Pósa}, Publ. Math. 9, 3-12 (1962; Zbl 0133.16701)].
Mathematics Subject Classification ID: 05B35
zbMATH DE Number: 1970691
reviewed by: Kelly J. Pearson
MaRDI profile type: Publication
cites work: Q5342984
cites work: THE LONG-LINE GRAPH OF A COMBINATORIAL GEOMETRY. I. EXCLUDING M(K4) AND THE (q + 2)-POINT LINE AS MINORS
cites work: Q4273835
cites work: Q3135082
description: scientific article; zbMATH DE number 1970691