A MATROID GENERALIZATION OF A RESULT OF DIRAC

Authors
OXLEY J
Citation
J. Oxley, A MATROID GENERALIZATION OF A RESULT OF DIRAC, Combinatorica, 17(2), 1997, pp. 267-273
Citations number
5
Categorie Soggetti
Mathematics, Pure",Mathematics
Journal title
Combinatorica → ACNP
ISSN journal
02099683
Volume
17
Issue
2
Year of publication
1997
Pages
267 - 273
Database
ISI
SICI code
0209-9683(1997)17:2<267:AMGOAR>2.0.ZU;2-R
Abstract
This paper generalizes a theorem of Dirac for graphs by proving that i f M is a 3-connected matroid, then, for all pairs {a, b} of distinct e lements of M and all cocircuits C of M, there is a circuit that conta ins {a, b} and meets C. It is also shown that, although the converse of this result fails, the specified condition call be used to characte rize 3-connected matroids.