In a matroid, (X, e) is a rooted circuit if X is a set not containing element e and X ∪ {e} is a circuit. We call X a broken circuit of e. A broken circuit clutter is the collection of broken circuits of a fixed element. Seymour [The matroids with the max-flow min-cut property, J. Combinatorial Theory B 23 (1977) 189–222] proved that a broken circuit… (More)