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Partitioning matroids with only small cocircuits. (English) Zbl 0996.05025
Let \(M\) be a matroid on the ground set \(E\) and suppose that the largest cocircuit of \(M\) has size \(c*\). The author shows that there is an integer \(n(c*)\) such that \(E\) can be partitioned into two sets \(E'\) and \(E''\) such that every connected component of each of the restrictions \(M|E'\) and \(M|E''\) has at most \(n(c*)\) elements. This theorem generalises analogue results for graphs (see the paper for details).

MSC:
05B35 Combinatorial aspects of matroids and geometric lattices
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