Non-separating cocircuits in binary matroids Original Research Article

In this note, we show that a 3-connected binary matroid M has at least r(M)−1 non-separating cocircuits avoiding a fixed element. As a consequence of this result, we get a lower bound for the number of non-separating cocircuits of a simple and a cosimple connected binary matroid that generalizes the bound obtained by McNulty and Wu.