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arXiv · 1705.08119

Distance bounds for graphs with some negative Bakry-\'Emery curvature

Shiping Liu·Florentin Münch·Norbert Peyerimhoff·Christian Rose
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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.

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Shiping Liu, Florentin Münch, Norbert Peyerimhoff, Christian Rose. 2017-05-23. Distance bounds for graphs with some negative Bakry-\'Emery curvature. https://doi.org/10.1515/agms-2019-0001

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