Total curvature of planar graphs with nonnegative combinatorial curvature

Total curvature of planar graphs with nonnegative combinatorial curvature

We prove that the total curvature of any planar graph with nonnegative combinatorial curvature is an integral multiple of 112\frac {1}{12}. As a corollary, this answers a question proposed by T. Réti.

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Veröffentlicht in:Transactions of the American Mathematical Society 2022-12, Vol.375 (12), p.8423-8444
Hauptverfasser: Hua, Bobo, Su, Yanhui
Format: Artikel
Sprache:eng
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Research article
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Zusammenfassung:We prove that the total curvature of any planar graph with nonnegative combinatorial curvature is an integral multiple of 112\frac {1}{12}. As a corollary, this answers a question proposed by T. Réti.
ISSN:0002-9947
1088-6850
DOI:10.1090/tran/8536