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Abstract
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We prove that the complement of any nonseparating planar graph of order
contains a
minor and argue that the order
is lowest possible with this property.
To illustrate the necessity of the nonseparating hypothesis, we give an example of a planar graph of order 11 whose
complement does not contain a
minor. We argue that the complements of planar graphs of order 11 are intrinsically
knotted. We compute the Hadwiger numbers of complements of wheel graphs.
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Keywords
graph minors, intrinsically knotted, nonseparating planar
graphs, Hadwiger number
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Mathematical Subject Classification
Primary: 05C10
Secondary: 57M15
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Milestones
Received: 2 May 2022
Revised: 15 July 2022
Accepted: 22 July 2022
Published: 10 August 2023
Communicated by Joel Foisy
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© 2023 MSP (Mathematical Sciences
Publishers). |
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