# A question from Jim Geelen about matroid circuits


I was asked a question recently, by Anna Lubiw and Vinayak Pathak, which led me to the following conjecture. It looks quite natural, so I wonder whether it is already known.

Conjecture: In any rank-$r$ matroid $M$, that has a circuit, there is a circuit $C$ such that each component of $M\con C$ has rank at most $r/2$.

I would be happy with $r/2$ replaced by $\alpha r$ for any $\alpha \lt 1$. The conjecture holds for graphic and cographic matroids.