We use cookies to ensure that we give you the best experience on our website. By continuing to browse this repository, you give consent for essential cookies to be used. You can read more about our Privacy and Cookie Policy.

Durham Research Online
You are in:

Bakry–Émery curvature and diameter bounds on graphs.

Liu, Shiping and Münch, Florentin and Peyerimhoff, Norbert (2018) 'Bakry–Émery curvature and diameter bounds on graphs.', Calculus of variations and partial differential equations., 57 (2). p. 67.


We prove finiteness and diameter bounds for graphs having a positive Ricci-curvature bound in the Bakry–Émery sense. Our first result using only curvature and maximal vertex degree is sharp in the case of hypercubes. The second result depends on an additional dimension bound, but is independent of the vertex degree. In particular, the second result is the first Bonnet–Myers type theorem for unbounded graph Laplacians. Moreover, our results improve diameter bounds from Fathi and Shu (Bernoulli 24(1):672–698, 2018) and Horn et al. (J für die reine und angewandte Mathematik (Crelle’s J), 2017, and solve a conjecture from Cushing et al. (Bakry–Émery curvature functions of graphs, 2016).

Item Type:Article
Full text:(AM) Accepted Manuscript
Download PDF
Publisher Web site:
Publisher statement:The final publication is available at Springer via
Date accepted:28 February 2018
Date deposited:01 May 2018
Date of first online publication:15 March 2018
Date first made open access:15 March 2019

Save or Share this output

Look up in GoogleScholar