Bricks and conjectures of Berge, Fulkerson and Seymour

Vahan Mkrtchyan; Eckhard Steffen

Bricks and conjectures of Berge, Fulkerson and Seymour

Discrete Mathematics 2010-03-31 v1

Authors: Vahan Mkrtchyan , Eckhard Steffen

Abstract

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.

Keywords

bricks r-graphs edge-colorings perfect matchings Seymour conjecture Berge conjecture Fulkerson conjecture counter-example

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@article{arxiv.1003.5782,
  title  = {Bricks and conjectures of Berge, Fulkerson and Seymour},
  author = {Vahan Mkrtchyan and Eckhard Steffen},
  journal= {arXiv preprint arXiv:1003.5782},
  year   = {2010}
}

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4 pages

Bricks and conjectures of Berge, Fulkerson and Seymour

Abstract

Keywords

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