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Minor-Minimal Planar Graphs of Even Branch-Width


Let k ≥ 1 be an integer, and let H be a graph with no isolated vertices embedded in the projective plane, such that every homotopically non-trivial closed curve intersects H at least k times, and the deletion and contraction of any edge in this embedding results in an embedding that no longer has this property. 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 in this way.

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Combinatorics, Probability and Computing
  • ISSN: 0963-5483
  • EISSN: 1469-2163
  • URL: /core/journals/combinatorics-probability-and-computing
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