Connected Hyperplanes in Binary Matroids

Involutions Of Connected Binary Matroids

We prove that if an involution φ is an automorphism of a connected binary matroid M , then there is a hyperplane of M that is invariant under φ. We also consider extensions of this result for higher connectivity.

On the matroids in which all hyperplanes are binary

Removing circuits in 3-connected binary matroids

For a k-connected graph or matroid M , where k is a fixed positive integer, we say that a subset X of E(M) is k-removable provided M\X is k-connected. In this paper, we obtain a sharp condition on the size of a 3connected binary matroid to have a 3-removable circuit.

Constructing Internally 4-connected Binary Matroids

In an earlier paper, we proved that an internally 4connected binary matroid with at least seven elements contains an internally 4-connected proper minor that is at most six elements smaller. We refine this result, by giving detailed descriptions of the operations required to produce the internally 4-connected minor. Each of these operations is top-down, in that it produces a smaller minor from ...

The 3-connected Binary Matroids with Circumference

In this paper, we construct all 3-connected binary matroids with circumference equal to 6 or 7 having large rank.