Total curvature of planar graphs with nonnegative combinatorial curvature

Hua, Bobo; Su, Yanhui

doi:10.1090/tran/8536

Total curvature of planar graphs with nonnegative combinatorial curvature
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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.

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