Liu, Shiping and Münch, Florentin and Peyerimhoff, Norbert and Rose, Christian (2019) 'Distance bounds for graphs with some negative Bakry-Émery curvature.', Analysis and geometry in metric spaces., 7 (1). pp. 1-14.
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.
| Item Type: | Article |
|---|---|
| Full text: | (VoR) Version of Record Available under License - Creative Commons Attribution. Download PDF (447Kb) |
| Status: | Peer-reviewed |
| Publisher Web site: | https://doi.org/10.1515/agms-2019-0001 |
| Publisher statement: | © 2019 Shiping Liu et al., published by De Gruyter. This work is licensed under the Creative Commons Attribution 4.0 Public License. BY 4.0 |
| Date accepted: | 29 January 2019 |
| Date deposited: | 11 April 2019 |
| Date of first online publication: | 22 March 2019 |
| Date first made open access: | No date available |
Save or Share this output
| Export: | |
| Look up in GoogleScholar |
