Minor-Minimal Planar Graphs of Even Branch-Width
Keyword(s):
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.
1975 ◽
Vol 77
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pp. 281-288
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Vol 28
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pp. 475-496
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pp. 55-60
2009 ◽
Vol 31
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pp. 267-278
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