Graphs with nonnegative Bakry-Émery curvature without Quadrilateral

2024/08/19 by Huiqiu Lin, Zhe You, Lin, Huiqiu +1 · 1 citation
Mathematics · Physics and Astronomy · #05C99 #51F99 #Advanced Differential Geometry Research #Combinatorics (math.CO) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematics and Applications #Metric Geometry (math.MG)

paper · pdf · doi:10.48550/arxiv.2408.09823

openalex publication_date 2024/08/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The definition of Ricci curvature on graphs in Bakry-Émery's sense based on curvature dimension condition was introduced by Lin and Yau [Math. Res. Lett., 2010]. Hua and Lin [Comm. Anal. Geom., 2019] classified unweighted graphs satisfying the curvature dimension condition CD(0,∞) whose girth are at least five. In this paper, we classify all of connected unweighted normalized C₄-free graphs satisfying curvature dimension condition CD(0,∞) for minimum degree at least 2 and the case with non-normalized Laplacian without degree condition..

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