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

Bobo Hua, Yanhui Su
2017 arXiv   pre-print
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.
arXiv:1709.05309v1 fatcat:ewlcyb3iuvdjhpzoiqjskbkxpu