Branchwidth of graphic matroids
Abstract
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.
Domains
Discrete Mathematics [cs.DM]Origin | Files produced by the author(s) |
---|
Loading...