A characterization of a class of non-binary matroids
type: Item
instance of: scholarly article
title: A characterization of a class of non-binary matroids
zbMATH Open document ID: 0658.05018
DOI: 10.1016/0095-8956(90)90025-U
published in: Journal of Combinatorial Theory. Series B
publication date: 1990-01-01T00:00:00Z
review text: A well-known result of \textit{W. T. Tutte} [Trans. Am. Math. Soc. 88, 144- 174 (1958; Zbl 0081.173)] is that the 4-point line is the only non-binary matroid such that, for every element e, both \(M\setminus e\) and M/e, the deletion and contraction of e from M, are binary. This paper characterizes those non-binary matroids M such that, for every element e, \(M\setminus e\) or M/e is binary. In particular, the main result proves that a 3-connected non-binary matroid whose rank and corank exceed two has the specified property if and only if it can be obtained from a 3- connected binary matroid by declaring a circuit-hyperplane of the latter to be independent.
Mathematics Subject Classification ID: 05B35
zbMATH DE Number: 4075082
zbMATH Keywords: circuit-hyperplane relaxation
zbMATH Keywords: non-binary matroid
author: James Oxley
reviewed by: James Oxley
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4075082