Non-separating cocircuits in matroids

Small cocircuits in matroids

We prove that, for any positive integers k, n, and q, if M is a simple matroid that has neither a U2,q+2nor an M(Kn)minor and M has sufficiently large rank, then M has a cocircuit of size at most r(M)/k.

Regular Matroids with Graphic Cocircuits

In this paper we examine the effect of removing cocircuits from regular matroids and we focus on the case in which such a removal always results in a graphic matroid. The first main result, given in section 3, is that a regular matroid with graphic cocircuits is signed-graphic if and only if it does not contain two specific minors. This provides a useful connection between graphic, regular and ...

Disjoint cocircuits in matroids with large rank

We prove that, for any positive integers n; k and q; there exists an integer R such that, if M is a matroid with no MðKnÞor U2;qþ2-minor, then either M has a collection of k disjoint cocircuits or M has rank at most R: Applied to the class of cographic matroids, this result implies the edge-disjoint version of the Erdös–Pósa Theorem. r 2002 Elsevier Science (USA). All rights reserved. AMS 1991 ...

Partitioning Matroids With Only Small Cocircuits

Spanning cycles in regular matroids without small cocircuits

A cycle of a matroid is a disjoint union of circuits. A cycle C of a matroidM is spanning if the rank of C equals the rank ofM . Settling an open problem of Bauer in 1985, Catlin in [P.A. Catlin, A reduction method to find spanning Eulerian subgraphs, J. Graph Theory 12 (1988) 29–44] showed that if G is a 2-connected graph on n > 16 vertices, and if δ(G) > n 5−1, thenGhas a spanning cycle. Catl...