Refined diameter bounds under curvature dimension conditions

TL;DR

This paper establishes explicit diameter bounds for graphs under curvature dimension conditions, refining previous results for finite dimensions, thereby advancing understanding of geometric properties in discrete structures.

Contribution

It provides a more precise diameter bound for graphs satisfying $CD(K,n)$ conditions, improving upon recent finite-dimensional results.

Findings

Explicit diameter bounds derived for graphs under $CD(K,n)$ conditions.

Refinement of previous diameter bounds for finite-dimensional cases.

Enhanced understanding of geometric constraints in graph theory.

Abstract

In this article we derive an explicit diameter bound for graphs satisfying the so-called curvature dimension conditions $CD(K,n)$. This refines a recent result due to Liu, M\"unch and Peyerimhoff when the dimension $n$ is finite.