English

Total curvature of planar graphs with nonnegative combinatorial curvature

Metric Geometry 2017-09-11 v2 Differential Geometry

Abstract

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. R\'eti.

Keywords

Cite

@article{arxiv.1703.04119,
  title  = {Total curvature of planar graphs with nonnegative combinatorial curvature},
  author = {Bobo Hua and Yanhui Su},
  journal= {arXiv preprint arXiv:1703.04119},
  year   = {2017}
}

Comments

24 pages, 21 figures