Minor-minimal planar graphs of even branch-width

Details Minor-minimal planar graphs of even branch-width Minor-minimal planar graphs of even branch-width

2010-07-02

arxiv.org/abs/1007.0373v2

Mathematics

Combinatorics

9 pages, to appear in Combinatorics, Probability and Computing

Scientific paper

Let k>0 be an integer, let H be a minor-minimal graph in the projective plane such that every homotopically non-trivial closed curve intersects H at least k times, and let G be the planar double cover of H obtained by lifting G into the universal covering space of the projective plane, the sphere. We prove that G is minor-minimal of branch-width 2k. We also exhibit examples of minor-minimal planar graphs of branch-width 6 that do not arise this way.

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