The first gap for total curvatures of planar graphs with nonnegative curvature |
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| Authors: | Bobo Hua Yanhui Su |
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| Institution: | 1. School of Mathematical Sciences, LMNS, Fudan University, Shanghai, China;2. College of Mathematics and Computer Science, Fuzhou University, Fuzhou, China |
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| Abstract: | We prove that the total curvature of a planar graph with nonnegative combinatorial curvature is at least 1/12 if it is positive. Moreover, we classify the metric structures of ambient polygonal surfaces for planar graphs attaining this bound. |
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| Keywords: | combinatorial curvature planar graphs total curvature |
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