Bricks and conjectures of Berge, Fulkerson and Seymour

V. Mkrtchyan, E. Steffen, ArXiv:1003.5782 (2010).

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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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arXiv:1003.5782
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Mkrtchyan V, Steffen E. Bricks and conjectures of Berge, Fulkerson and Seymour. arXiv:10035782. 2010.
Mkrtchyan, V., & Steffen, E. (2010). Bricks and conjectures of Berge, Fulkerson and Seymour. ArXiv:1003.5782.
@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} }
Mkrtchyan, Vahan, and Eckhard Steffen. “Bricks and Conjectures of Berge, Fulkerson and Seymour.” ArXiv:1003.5782, 2010.
V. Mkrtchyan and E. Steffen, “Bricks and conjectures of Berge, Fulkerson and Seymour,” arXiv:1003.5782. 2010.
Mkrtchyan, Vahan, and Eckhard Steffen. “Bricks and Conjectures of Berge, Fulkerson and Seymour.” ArXiv:1003.5782, 2010.

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