Gauss-Bonnet formula, finiteness condition, and characterizations of graphs embedded in surfaces

DOI10.1007/s00373-008-0782-zzbMath1170.05011OpenAlexW2030361849MaRDI QIDQ1015427

Guantao Chen, Beifang Chen

Publication date: 8 May 2009

Published in: Graphs and Combinatorics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00373-008-0782-z

zbMATH Keywords

embeddinginfinite graphGauss-Bonnet formulafiniteness theoremcombinatorial curvatureEuler relationface style

Mathematics Subject Classification ID

Related Items (17)

Total curvature of planar graphs with nonnegative combinatorial curvature ⋮ Curvature notions on graphs ⋮ On the number of vertices of positively curved planar graphs ⋮ Topological self-organization of strongly interacting particles ⋮ Geometric and Spectral Consequences of Curvature Bounds on Tessellations ⋮ On the \(l^p\) spectrum of Laplacians on graphs ⋮ The set of vertices with positive curvature in a planar graph with nonnegative curvature ⋮ Curvature, geometry and spectral properties of planar graphs ⋮ An overview of curvature bounds and spectral theory of planar tessellations ⋮ Cubic graphs and the golden mean ⋮ A curvature notion for planar graphs stable under planar duality ⋮ A result on combinatorial curvature for embedded graphs on a surface ⋮ The Gauss-Bonnet formula of polytopal manifolds and the characterization of embedded graphs with nonnegative curvature ⋮ Geometric analysis aspects of infinite semiplanar graphs with nonnegative curvature II ⋮ Hyperbolic polyhedral surfaces with regular faces ⋮ On the largest planar graphs with everywhere positive combinatorial curvature ⋮ Some criteria for circle packing types and combinatorial Gauss-Bonnet Theorem

Cites Work

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• The Gram-Sommerville and Gauss-Bonnet theorems and combinatorial geometric measures for noncompact polyhedra
• A combinatorial analogue of a theorem of Myers
• Bochner's method for cell complexes and combinatorial Ricci curvature
• On the curvature of piecewise flat spaces
• Critical points and curvature for embedded polyhedra
• E ₁₁ and M theory
• Positively curved cubic plane graphs are finite
• An analogue of the Descartes-Euler formula for infinite graphs and Higuchi’s conjecture
• Combinatorics of Triangulations of 3-Manifolds
• Combinatorial curvature for planar graphs

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