Distance Bounds for Graphs with Some Negative Bakry-Émery Curvature

Liu, Shiping; Münch, Florentin; Peyerimhoff, Norbert; Rose, Christian

Abstract

We prove distance bounds for graphs possessing positive Bakry-Émery 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-Émery curvature assumptions on graphs.

Citation

Liu, S., Münch, F., Peyerimhoff, N., & Rose, C. (2019). Distance Bounds for Graphs with Some Negative Bakry-Émery Curvature. Analysis and Geometry in Metric Spaces, 7(1), 1-14. https://doi.org/10.1515/agms-2019-0001

• Journal Article Type: Article
• Acceptance Date: Jan 29, 2019
• Online Publication Date: Mar 22, 2019
• Publication Date: Mar 31, 2019
• Deposit Date: Apr 11, 2019
• Publicly Available Date: Apr 11, 2019
• Journal: Analysis and Geometry in Metric Spaces
• Publisher: De Gruyter Open
• Peer Reviewed: Peer Reviewed
• Volume: 7
• Issue: 1
• Pages: 1-14
• DOI: https://doi.org/10.1515/agms-2019-0001