Une relation de séparation entre cocircuits d'un matroide

Let S₁′S₂′S₃′ be 3 distinct cocircuits of a matroid M on a set E. We say that S₁′ does not separate S₂′ and S₃′ when S₂′S₁′ and S₃′S₁′ are included in one single and the same component of the submatroid M × (ES₁′). Our main result is: A matroid is graphic if and only if from any 3 cocircuits having a non-empty intersection there is at least one which separates the two others.