Spanning cycles in regular matroids without small cocircuits

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 ...

Spanning cycles in regular matroids without M*(K5) minors

Catlin and Jaeger proved that the cycle matroid of a 4-edge-connected graph has a spanning cycle. This result can not be generalized to regular matroids as there exist infinitely many connected cographic matroids, each of which contains a M(K5) minor and has arbitrarily large cogirth, that do not have spanning cycles. In this paper, we proved that if a connected regular matroid without aM(K5)-m...

Circuits Through Cocircuits In A Graph With Extensions To Matroids

We show that for any k-connected graph having cocircumference c∗, there is a cycle which intersects every cocycle of size c∗ − k+2 or greater. We use this to show that in a 2connected graph, there is a family of at most c∗ cycles for which each edge of the graph belongs to at least two cycles in the family. This settles a question raised by Oxley. A certain result known for cycles and cocycles ...

Partitioning Matroids With Only Small Cocircuits

The Erdös-Pósa property for matroid circuits

The number of disjoint cocircuits in a matroid is bounded by its rank. There are, however, matroids with arbitrarily large rank that do not contain two disjoint cocircuits; consider, for example, M(Kn) and Un,2n. Also the bicircular matroids B(Kn) have arbitrarily large rank and have no 3 disjoint cocircuits. We prove that for each k and n there exists a constant c such that, if M is a matroid ...