Title

On connectivity in matroids and graphs

Document Type

Article

Publication Date

1-1-1981

Abstract

In this paper we derive several results for connected matroids and use these to obtain new results for 2-connected graphs. In particular» we generalizework of Murty and Seymour on the number of two-element cocircuits in aminimally connected matroid, and work of Dirac, Plummer and Mader on thenumber of vertices of degree two in a minimally 2-connected graph. We also solvea problem of Murty by giving a straightforward but useful characterization ofminimally connected matroids. The final part of the paper gives a matroidgeneralization of Dirac and Plummer’s result that every minimally 2-connectedgraph is 3-colourable. © 1981 American Mathematical Society.

Publication Source (Journal or Book title)

Transactions of the American Mathematical Society

First Page

47

Last Page

58

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