A result on combinatorial curvature for embedded graphs on a surface

DOI10.1016/j.disc.2007.11.007zbMath1161.05031OpenAlexW2082676938MaRDI QIDQ998402

Li-Li Zhang

Publication date: 28 January 2009

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.disc.2007.11.007

zbMATH Keywords

Gauss-Bonnet formulaEmbeddingEuler relationCombinatorial curvatureFace cycleFiniteness theoremInfinite graph

Mathematics Subject Classification ID

Planar graphs; geometric and topological aspects of graph theory (05C10)

Related Items (12)

Total curvature of planar graphs with nonnegative combinatorial curvature ⋮ Curvature notions on graphs ⋮ On the number of vertices of positively curved planar graphs ⋮ Doubly semi-equivelar maps on the plane and the torus ⋮ Extremal \(\{ p, q\}\)-animals ⋮ Geometric and Spectral Consequences of Curvature Bounds on Tessellations ⋮ The set of vertices with positive curvature in a planar graph with nonnegative curvature ⋮ Sectional curvature of polygonal complexes with planar substructures ⋮ An overview of curvature bounds and spectral theory of planar tessellations ⋮ A curvature notion for planar graphs stable under planar duality ⋮ Hyperbolic polyhedral surfaces with regular faces ⋮ On the largest planar graphs with everywhere positive combinatorial curvature

Cites Work

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• Gauss-Bonnet formula, finiteness condition, and characterizations of graphs embedded in surfaces
• The Gram-Sommerville and Gauss-Bonnet theorems and combinatorial geometric measures for noncompact polyhedra
• Digital curvature flow and its application for skeletonization
• On the curvature of piecewise flat spaces
• Critical points and curvature for embedded polyhedra
• Locally finite, planar, edge-transitive graphs

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