On connectivity in matroids and graphs
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
Oxley, J. (1981). On connectivity in matroids and graphs. Transactions of the American Mathematical Society, 265 (1), 47-58. https://doi.org/10.1090/S0002-9947-1981-0607106-5