Halin graphs with positive Lin-Lu-Yau curvature

2025/05/07 by Chen, Kaizhe, Lin, Huiqiu, Liu, Shiping +1
#05C10 #05C81 #51F99 #Combinatorics (math.CO) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2505.04470

Abstract

Halin graphs constitute an interesting class of planar and polyhedral graphs. A generalized Halin graph is obtained by connecting all leaves of a planar embedding of a tree via a cycle. A Halin graph is a generalized Halin graph having no vertex of degree two. We classify all generalized Halin graphs with positive Lin-Lu-Yau curvature.

Citations

• On the size of outerplanar graphs with positive Lin-Lu-Yau Ricci curvature
• Outerplanar graphs with positive Lin-Lu-Yau curvature
• On the size of planar graphs with positive Lin-Lu-Yau Ricci curvature
• Ollivier Ricci curvature for general graph Laplacians: Heat equation,\n Laplacian comparison, non-explosion and diameter bounds
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• Ollivier--Ricci Idleness Functions of Graphs
• Ricci-flat graphs with girth at least five
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• Ricci curvature of Markov chains on metric spaces

Related

• Drawing Halin-graphs with small height
• Halin graphs are 3-vertex-colorable except even wheels
• Minimum degree condition for spanning generalized Halin graphs
• Outerplanar graphs with positive Lin-Lu-Yau curvature
• Graphs with positive Lin-Lu-Yau curvature without quadrilaterals