All Outputs (4)

Bakry-Émery curvature on graphs as an eigenvalue problem (2022)
Journal Article
Cushing, D., Kamtue, S., Liu, S., & Peyerimhoff, N. (2022). Bakry-Émery curvature on graphs as an eigenvalue problem. Calculus of Variations and Partial Differential Equations, 61, Article 62. https://doi.org/10.1007/s00526-021-02179-z

In this paper, we reformulate the Bakry-Émery curvature on a weighted graph in terms of the smallest eigenvalue of a rank one perturbation of the so-called curvature matrix using Schur complement. This new viewpoint allows us to show various curvatur... Read More about Bakry-Émery curvature on graphs as an eigenvalue problem.

Rigidity of the Bonnet-Myers inequality for graphs with respect to Ollivier Ricci curvature (2020)
Journal Article
Cushing, D., Kamtue, S., Liu, S., Muench, F., & Peyerimhoff, N. (2020). Rigidity of the Bonnet-Myers inequality for graphs with respect to Ollivier Ricci curvature. Advances in Mathematics, 360, Article 107188. https://doi.org/10.1016/j.aim.2020.107188

We introduce the notion of Bonnet-Myers and Lichnerowicz sharpness in the Ollivier Ricci curvature sense. Our main result is a classification of all self-centered Bonnet-Myers sharp graphs (hypercubes, cocktail party graphs, even-dimensional demi-cub... Read More about Rigidity of the Bonnet-Myers inequality for graphs with respect to Ollivier Ricci curvature.

Quartic graphs which are Bakry-Émery curvature sharp (2019)
Journal Article
Cushing, D., Kamtue, S., Peyerimhoff, N., & Watson May, L. (2020). Quartic graphs which are Bakry-Émery curvature sharp. Discrete Mathematics, 343(3), Article 111767. https://doi.org/10.1016/j.disc.2019.111767

We give a classification of all connected quartic graphs which are (infinity) curvature sharp in all vertices with respect to Bakry-Émery curvature. The result is based on a computer classification by F. Gurr and L. Watson May and a combinatorial cas... Read More about Quartic graphs which are Bakry-Émery curvature sharp.

Long-Scale Ollivier Ricci Curvature of Graphs (2019)
Journal Article
Cushing, D., & Kamtue, S. (2019). Long-Scale Ollivier Ricci Curvature of Graphs. Analysis and Geometry in Metric Spaces, 7(1), 22-44. https://doi.org/10.1515/agms-2019-0003

We study the long-scale Ollivier Ricci curvature of graphs as a function of the chosen idleness. Similarly to the previous work on the short-scale case, we show that this idleness function is concave and piecewise linear with at most 3 linear parts.... Read More about Long-Scale Ollivier Ricci Curvature of Graphs.