Distance bounds for graphs with some negative Bakry-Émery curvature

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.

arXiv comment19 pages

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Cited by in corpus (4)

• Gradient estimates, Bakry-Emery Ricci curvature and ellipticity for unbounded graph Laplacians
• Li-Yau inequality under $CD(0,n)$ on graphs
• Perpetual cutoff method and discrete Ricci curvature bounds with exceptions
• Coverings and the heat equation on graphs: stochastic incompleteness, the Feller property and uniform transience