Branchwidth of graphic matroids

Frédéric Mazoit (1) , Stéphan Thomassé (2)

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique
2 ALGCO - Algorithmes, Graphes et Combinatoire

Answering a question of Geelen, Gerards, Robertson and Whittle, we prove that the branchwidth of a bridgeless graph is equal to the branchwidth of its cycle matroid. Our proof is based on branch-decompositions of hypergraphs. By matroid duality, a direct corollary of this result is that the branchwidth of a bridgeless planar graph is equal to the branchwidth of its planar dual. This consequence was a direct corollary of a result by Seymour and Thomas.

Domaines: Mathématique discrète [cs.DM]

Frédéric Mazoit, Stéphan Thomassé. Branchwidth of graphic matroids. Surveys in Combinatorics 2007, 346, pp.275-286, 2007, 9780511666209. ⟨10.1017/CBO9780511666209.010⟩. ⟨lirmm-00325145⟩