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The set of vertices with positive curvature in a planar graph with nonnegative curvature

Bobo Hua School of Mathematical Sciences, LMNS, Fudan University, Shanghai 200433, China; Shanghai Center for Mathematical Sciences, Fudan University, Shanghai 200433, China Yanhui Su College of Mathematics and Computer Science, Fuzhou University, Fuzhou 350116, China

Combinatorics Differential Geometry mathscidoc:2203.06003

Advances in Mathematics, 343, 789-820, 2019.2
In this paper, we give the sharp upper bound for the number of vertices with positive curvature in a planar graph with nonnegative combinatorial curvature. Based on this, we show that the automorphism group of a planar—possibly infinite—graph with nonnegative combinatorial curvature and positive total curvature is a finite group, and give an upper bound estimate for the order of the group.
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@inproceedings{bobo2019the,
  title={The set of vertices with positive curvature in a planar graph with nonnegative curvature},
  author={Bobo Hua, and Yanhui Su},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220318131640735512009},
  booktitle={Advances in Mathematics},
  volume={343},
  pages={789-820},
  year={2019},
}
Bobo Hua, and Yanhui Su. The set of vertices with positive curvature in a planar graph with nonnegative curvature. 2019. Vol. 343. In Advances in Mathematics. pp.789-820. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220318131640735512009.
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