The first gap for total curvatures of planar graphs with nonnegative curvature

Bobo Hua; Yanhui Su

The first gap for total curvatures of planar graphs with nonnegative curvature

Combinatorics 2017-09-18 v1

Authors: Bobo Hua , Yanhui Su

Abstract

We prove that the total curvature of a planar graph with nonnegative combinatorial curvature is at least $\frac{1}{12}$ if it is positive. Moreover, we classify the metric structures of ambient polygonal surfaces for planar graphs attaining this bound.

Keywords

planar graph nonnegative curvature total curvature combinatorial curvature polygonal surfaces

Cite

@article{arxiv.1709.05309,
  title  = {The first gap for total curvatures of planar graphs with nonnegative curvature},
  author = {Bobo Hua and Yanhui Su},
  journal= {arXiv preprint arXiv:1709.05309},
  year   = {2017}
}

Comments

Much of this article was previously contained as arXiv:1703.04119v1, which was split into 1703.04119v2 (and any subsequent version) and this present article

The first gap for total curvatures of planar graphs with nonnegative curvature

Abstract

Keywords

Cite

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