Abstract
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).
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