On the matroids in which all hyperplanes are binary
type: Item
instance of: scholarly article
title: On the matroids in which all hyperplanes are binary
zbMATH Open document ID: 0865.05028
DOI: 10.1016/0012-365X(95)00166-T
author: S. R. Kingan
author: James Oxley
published in: Discrete Mathematics
publication date: 1997-06-19T00:00:00Z
review text: The main result of this paper is the following theorem: Let \(\mathcal M\) be a minor-closed class of matroids, and let \({\mathcal M}_1\) be the class of matroids for which the restriction to every hyperplane is in \(\mathcal M\). Then \({\mathcal M}_1\) is minor-closed and its set of excluded minors is \(\{ U_{1,1} \oplus N: N \hbox{ is an excluded minor for } {\mathcal M} \}\). This result is applied to matroids in which the restriction to every hyperplane is binary. Several alternative characterizations of this class of matroids are provided.
Mathematics Subject Classification ID: 05B35
zbMATH DE Number: 955163
zbMATH Keywords: matroids
zbMATH Keywords: hyperplane
zbMATH Keywords: excluded minors
reviewed by: Esther R. Lamken
MaRDI profile type: Publication
cites work: Q5790167
cites work: Q5619114
cites work: Q3765790
cites work: Fundamental circuits and a characterization of binary matroids
cites work: Q3135082
cites work: Lectures on matroids
cites work: Q4111952
full work available at URL: 0012-365x(95)00166-t
OpenAlex ID: W2108673614
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description: scientific article; zbMATH DE number 955163