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Links in
projective planar graphs
Joel Foisy, Luis Ángel Topete Galván, Evan Knowles, Uriel Alejandro Nolasco, Yuanyuan Shen and Lucy Wickham |
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Vol. 18 (2025), No. 2, 199–238
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Abstract |
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A graph is nonseparating projective planar if has a projective planar embedding without a nonsplit link. Nonseparating projective planar graphs are closed under taking minors and are a superclass of projective outerplanar graphs. We partially characterize the minor-minimal separating projective planar graphs by proving that given a minor-minimal nonouter-projective-planar graph , either is minor-minimal separating projective planar or is minor-minimal weakly separating projective planar, a necessary condition for to be separating projective planar. One way to generalize separating projective planar graphs is to consider type I 3-links consisting of two cycles and a pair of vertices. A graph is intrinsically projective planar type I 3-linked (IPPI3L) if its every projective planar embedding contains a nonsplit type I 3-link. We partially characterize minor-minimal IPPI3L graphs by classifying all minor-minimal IPPI3L graphs with three or more components, and finding many others with fewer components. |
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Keywords
separating graphs, projective planar graphs, projective
planar links
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Mathematical Subject Classification
Primary: 05C10, 57M15
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Milestones
Received: 13 June 2022
Revised: 15 August 2023
Accepted: 15 September 2023
Published: 26 February 2025
Communicated by Kenneth S. Berenhaut
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Authors |
| Joel Foisy | |
| Department of Mathematics SUNY Potsdam Potsdam, NY United States |
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| Luis Ángel Topete Galván | |
| Faculty of Sciences Universidad Nacional Autónoma de México Pachuca de Soto Mexico |
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| Evan Knowles | |
| SUNY Potsdam Potsdam, NY United States |
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| Uriel Alejandro Nolasco | |
| Universidad Autonomo del Estato de
Hidalgo Tequixquiac Mexico |
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| Yuanyuan Shen | |
| Department of Mathematics University of Pennsylvania Philadelphia, PA United States |
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| Lucy Wickham | |
| Department of Mathematics Syracuse University Syracuse, NY United States |
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| © 2025 MSP (Mathematical Sciences Publishers). |
