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Distance bounds for graphs with some negative Bakry-Émery curvature.

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.


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.

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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

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