# zbMATH — the first resource for mathematics

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
##### Keywords:
partitioning matroids; chromatic theory of graphs
Full Text: