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

2020/10/08 by Linyuan Lü, Zhiyu Wang, Lu, Linyuan +1 · 1 citation
Mathematics · #05C10 #51F99 #Combinatorics (math.CO) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2010.03716

openalex publication_date 2020/10/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 Δ(G)≤ 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.

Citations

• Ricci curvature of Markov chains on metric spaces

Cited by

• Edge-connectivity and non-negative Lin-Lu-Yau curvature

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