Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



On connectivity in matroids and graphs

Author: James G. Oxley
Journal: Trans. Amer. Math. Soc. 265 (1981), 47-58
MSC: Primary 05B35; Secondary 05C40
MathSciNet review: 607106
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we derive several results for connected matroids and use these to obtain new results for -connected graphs. In particular, we generalize work of Murty and Seymour on the number of two-element cocircuits in a minimally connected matroid, and work of Dirac, Plummer and Mader on the number of vertices of degree two in a minimally $ 2$-connected graph. We also solve a problem of Murty by giving a straightforward but useful characterization of minimally connected matroids. The final part of the paper gives a matroid generalization of Dirac and Plummer's result that every minimally $ 2$-connected graph is $ 3$-colourable.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 05B35, 05C40

Retrieve articles in all journals with MSC: 05B35, 05C40

Additional Information

Article copyright: © Copyright 1981 American Mathematical Society

American Mathematical Society