On the size of planar graphs with positive Lin-Lu-Yau Ricci curvature

Abstract

We show that if a planar graph $G$ with minimum degree at least $3$ has positive Lin-Lu-Yau Ricci curvature on every edge, then $\Delta (G)\le 17$, which then implies that $G$ is finite. This is an analogue of a result of DeVos and Mohar [{\em Trans. Amer. Math. Soc., 2007}] on the size of planar graphs with positive combinatorial curvature.

10 pages, 2 figures

References in corpus (1)

• A new Poisson-type deviation inequality for Markov jump processes with positive Wasserstein curvature