{"abstract":[{"lang":"eng","text":"An $r$-graph is an $r$-regular graph where every odd set of vertices is\r\nconnected by at least $r$ edges to the rest of the graph. Seymour conjectured\r\nthat any $r$-graph is $r+1$-edge-colorable, and also that any $r$-graph\r\ncontains $2r$ perfect matchings such that each edge belongs to two of them. We\r\nshow that the minimum counter-example to either of these conjectures is a\r\nbrick. Furthermore we disprove a variant of a conjecture of Fan, Raspaud."}],"_id":"10202","citation":{"apa":"Mkrtchyan, V., &#38; Steffen, E. (2010). Bricks and conjectures of Berge, Fulkerson and Seymour. <i>ArXiv:1003.5782</i>.","ieee":"V. Mkrtchyan and E. Steffen, “Bricks and conjectures of Berge, Fulkerson and Seymour,” <i>arXiv:1003.5782</i>. 2010.","chicago":"Mkrtchyan, Vahan, and Eckhard Steffen. “Bricks and Conjectures of Berge, Fulkerson and Seymour.” <i>ArXiv:1003.5782</i>, 2010.","mla":"Mkrtchyan, Vahan, and Eckhard Steffen. “Bricks and Conjectures of Berge, Fulkerson and Seymour.” <i>ArXiv:1003.5782</i>, 2010.","short":"V. Mkrtchyan, E. Steffen, ArXiv:1003.5782 (2010).","bibtex":"@article{Mkrtchyan_Steffen_2010, title={Bricks and conjectures of Berge, Fulkerson and Seymour}, journal={arXiv:1003.5782}, author={Mkrtchyan, Vahan and Steffen, Eckhard}, year={2010} }","ama":"Mkrtchyan V, Steffen E. Bricks and conjectures of Berge, Fulkerson and Seymour. <i>arXiv:10035782</i>. 2010."},"publication":"arXiv:1003.5782","date_updated":"2022-01-06T06:50:31Z","status":"public","date_created":"2019-06-07T13:10:04Z","title":"Bricks and conjectures of Berge, Fulkerson and Seymour","year":"2010","author":[{"first_name":"Vahan","full_name":"Mkrtchyan, Vahan","last_name":"Mkrtchyan"},{"id":"15548","first_name":"Eckhard","last_name":"Steffen","full_name":"Steffen, Eckhard"}],"type":"preprint","language":[{"iso":"eng"}],"user_id":"15540"}