Cocircuit coverings and packings for binary matroids
JAMES G. OXLEY · Mathematical Proceedings of the Cambridge Philosophical Society · 1978
If M is an arbitrary loopless matroid with ground set E ( M ) and rank function ρ, then let α( M ) be the minimum size of a set of cocircuits of M , whose union is E ( M ), and let β( M ) be the maximum size of a set of pairwise disjoint cocircuits of M . The following conjecture is based on Gallai's theorem that the vertex-stability and vertex-covering numbers of a graph G sum to the number of vertices of G (1).