Hostname: page-component-74656f9884-kv2lp Total loading time: 0 Render date: 2026-11-06T09:59:19.083Z Has data issue: false hasContentIssue false
  • English
  • Français

Non-Binary Matroids Having At Most Three Non-Binary Elements

Published online by Cambridge University Press:  12 September 2008

Manoel Lemos
Manoel Lemos
Affiliation:
Departamento de Matemática, Universidade Federal de Pernambuco Cidade Universitária, Recife, PE, 50740–540, Brazil e-mail: manoel@dmat.ufpe.br
Get access Rights & Permissions [Opens in a new window]

Abstract

An element e of a matroid M is called non-binary when M\e and M/e are both non-binary matroids. Oxley in [5] gave a characterization of the 3-connected non-binary matroids without non-binary elements. In this paper, we will construct all the 3-connected matroids having 1, 2 or 3 non-binary elements.

Information

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 3 , Issue 3 , September 1994 , pp. 355 - 369
Copyright
Copyright © Cambridge University Press 1994

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

[1]Bixby, R. E. (1974) 1-matrices and a characterization of binary matroid. Discrete Math. 8 139–145.CrossRefGoogle Scholar
[2]Bixby, R. E. (1982) A simple theorem on 3-connectivity. Linear Algebra Appl. 45 123–126.CrossRefGoogle Scholar
[3]Crapo, H. H. (1965) Single-element extensions of matroids. J. Res. Nat. Bur. Standards, Sect. B 69 55–65.CrossRefGoogle Scholar
[4]Oxley, J. G. (1987) On nonbinary 3-connected matroids. Transactions of the American Mathematical Society 300 663–679.Google Scholar
[5]Oxley, J. G. (1990) A characterization of a class of non-binary matroids. J. Combin. Theory, Ser. B 49 181–189.CrossRefGoogle Scholar
[6]Oxley, J. G. (1992) Matroid Theory, Oxford University Press.Google Scholar
[7]Seymour, P. D. (1980) Decomposition of regular matroids. J. Combin. Theory, Ser. B 28 305–359.CrossRefGoogle Scholar
[8]Seymour, P. D. (1981) On minors of non-binary matroids. Combinatorica 1 387–394.CrossRefGoogle Scholar
[9]Tutte, W. T. (1965) Lectures on matroids. J. Res. Nat. Bur. Standards, Sect. B 69 1–47.Google Scholar
[10]Tutte, W. T. (1966) Connectivity in matroids. Canad. J. Math. 18 1301–1324.CrossRefGoogle Scholar
[11]Welsh, D. J. A. (1976) Matroid Theory, Academic Press.Google Scholar