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Minor-Minimal Planar Graphs of Even Branch-Width

Published online by Cambridge University Press:  03 September 2010

TORSTEN INKMANN  and
ROBIN THOMAS
TORSTEN INKMANN
Affiliation:
School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332-0160, USA (e-mail: torsten.inkmann@gmail.com, thomas@math.gatech.edu)
ROBIN THOMAS
Affiliation:
School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332-0160, USA (e-mail: torsten.inkmann@gmail.com, thomas@math.gatech.edu)
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Abstract

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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Type
Paper
Information
Combinatorics, Probability and Computing , Volume 20 , Issue 1 , January 2011 , pp. 73 - 82
Copyright
Copyright © Cambridge University Press 2010

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