Bricks and conjectures of Berge, Fulkerson and Seymour
Mkrtchyan, Vahan · Steffen, Eckhard
Original · EN
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+1-edge-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.
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