Bricks and conjectures of Berge, Fulkerson and Seymour

An r-graph is an r-regular graph where every odd set of vertices is connected by at least r edges to the rest of the graph. Seymour conjectured that any r-graph is r + 1edge-colorable, and also that any r-graph contains 2r perfect matchings such that each edge belongs to two of them. We show that the minimum counter-example to either of these conjectures is a brick. Furthermore we disprove a variant of a conjecture of Fan, Raspaud.