Work

On the classification of regular graphs with positive Lin-Lu-Yau curvature

Year: 2026

Type: preprint

Abstract: We prove several new structural and classification results about $d$-regular graphs with positive Lin--Lu--Yau (LLY) curvature. We show that any positively curved $d$-regular graph has diameter at most $2d-2$, which improves the previously best known diameter bound obtained from the Bonnet-Myers-type theorem for positively curved graphs. We further show that every positively curved $d$-regular graph with $d\ge 3$ is $3$-connected. We classify all positively curved $3$-regular graphs, as well as all positively curved regular planar graphs.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.08903

Authors: Brooks, George, Johnson, Nathanael, Linz, William, Liu, Xiaonan, Lu, Linyuan, Vaughn, Wynton

Institutions: University of South Carolina, The Ohio State University, University of Memphis, Louisiana State University, Clemson University

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, University of South Carolina

Award: RTG: Mathematical Foundation of Data Science at University of South Carolina

OpenAlex ID: W7212017199

Cites: 2

Cited by: 2

Related to: 10