Branchwidth of graphic matroids

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.

[1]  Paul D. Seymour,et al.  Graph minors. X. Obstructions to tree-decomposition , 1991, J. Comb. Theory, Ser. B.

[2]  Bert Gerards,et al.  On the excluded minors for the matroids of branch-width k , 2003, J. Comb. Theory, Ser. B.

[3]  Illya V. Hicks,et al.  The branchwidth of graphs and their cycle matroids , 2007, J. Comb. Theory, Ser. B.

[4]  Robin Thomas,et al.  Call routing and the ratcatcher , 1994, Comb..

[5]  B. Mohar,et al.  Graph Minors , 2009 .

[6]  Ioan Todinca,et al.  Chordal embeddings of planar graphs , 2003, Discret. Math..