Distance bounds for graphs with some negative Bakry-\'Emery curvature
Differential Geometry
2019-03-26 v2
Abstract
We prove distance bounds for graphs possessing positive Bakry-\'Emery curvature apart from an exceptional set, where the curvature is allowed to be non-positive. If the set of non-positively curved vertices is finite, then the graph admits an explicit upper bound for the diameter. Otherwise, the graph is a subset of the tubular neighborhood with an explicit radius around the non-positively curved vertices. Those results seem to be the first assuming non-constant Bakry-\'Emery curvature assumptions on graphs.
Cite
@article{arxiv.1705.08119,
title = {Distance bounds for graphs with some negative Bakry-\'Emery curvature},
author = {Shiping Liu and Florentin Münch and Norbert Peyerimhoff and Christian Rose},
journal= {arXiv preprint arXiv:1705.08119},
year = {2019}
}
Comments
19 pages