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

TL;DR

This paper proves that outerplanar graphs with minimum degree at least 2 and positive Lin-Lu-Yau Ricci curvature on all vertex pairs have at most 10 vertices, establishing a sharp upper bound.

Contribution

It extends previous results by showing a sharp size bound for such graphs with positive Ricci curvature.

Findings

Outerplanar graphs with positive Ricci curvature have at most 10 vertices.

The bound of 10 vertices is sharp.

The result generalizes earlier work by Brooks et al.

Abstract

In this paper, extending a result of Brooks et.al. [arXiv:2403.04110], we show that if an outerplanar graph $G$ with minimum degree at least $2$ has positive Lin-Lu-Yau curvature on every vertex pair, then $G$ has at most $10$ vertices, and this upper bound is sharp.