## Total curvature of planar graphs with nonnegative combinatorial curvature

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- by Bobo Hua and Yanhui Su PDF
- Trans. Amer. Math. Soc.
**375**(2022), 8423-8444 Request permission

## Abstract:

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

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## Additional Information

**Bobo Hua**- Affiliation: School of Mathematical Sciences, LMNS, Fudan University, Shanghai 200433, People’s Republic of China
- MR Author ID: 865783
- Email: bobohua@fudan.edu.cn
**Yanhui Su**- Affiliation: School of Mathematics and Statistics, Fuzhou University, Fuzhou 350116, People’s Republic of China; and Key Laboratory of Operations Research and Control of Universities in Fujian, Fuzhou, People’s Republic of China
- MR Author ID: 961522
- ORCID: 0000-0001-6534-024X
- Email: suyh@fzu.edu.cn
- Received by editor(s): March 18, 2019
- Received by editor(s) in revised form: July 18, 2021
- Published electronically: September 29, 2022
- Additional Notes: The first author was supported by NSFC, grant no. 11831004 and grant no. 11401106. The second author was supported by NSFC, grant no. 11771083 and NSF of Fujian Province through Grants 2021J01615, 2017J01556 and 2016J01013
- © Copyright 2022 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**375**(2022), 8423-8444 - MSC (2020): Primary 05C10
- DOI: https://doi.org/10.1090/tran/8536