Bricks and conjectures of Berge, Fulkerson and Seymour Mkrtchyan, Vahan Steffen, Eckhard 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. 2010 info:eu-repo/semantics/preprint doc-type:preprint text http://purl.org/coar/resource_type/c_816b https://ris.uni-paderborn.de/record/10202 Mkrtchyan V, Steffen E. Bricks and conjectures of Berge, Fulkerson and Seymour. <i>arXiv:10035782</i>. 2010. eng info:eu-repo/semantics/closedAccess