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Complete minors
in complements of nonseparating planar graphs
Leonard Fowler, Gregory Li and Andrei Pavelescu |
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Vol. 16 (2023), No. 3, 505–518
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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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Authors |
| Leonard Fowler | |
| Rensselaer Polytechnic
Institute Troy, NY United States |
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| Gregory Li | |
| Harvard University Cambridge, MA United States |
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| Andrei Pavelescu | |
| Department of Mathematics and
Statistics University of South Alabama Mobile, AL United States |
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| © 2023 MSP (Mathematical Sciences Publishers). |
