A new proof of Laman's theorem

DOI10.1007/BF02988323zbMath0786.05069OpenAlexW2062020888MaRDI QIDQ1313353

Tiong Seng Tay

Publication date: 2 May 1994

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

Full work available at URL: https://doi.org/10.1007/bf02988323

zbMATH Keywords

characterizationplaneLaman's theoremgenerically rigid bar frameworks

Mathematics Subject Classification ID

Trees (05C05) Planar graphs; geometric and topological aspects of graph theory (05C10) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) (05C70) Structural characterization of families of graphs (05C75) Rigidity and flexibility of structures (aspects of discrete geometry) (52C25) Euclidean analytic geometry (51N20)

Related Items (9)

Symmetric versions of Laman's theorem ⋮ Slider-pinning rigidity: a Maxwell-Laman-type theorem ⋮ Motions of grid-like reflection frameworks ⋮ A rooted-forest partition with uniform vertex demand ⋮ Symmetric isostatic frameworks with \(\ell^1\) or \(\ell^\infty\) distance constraints ⋮ On the generic rigidity of bar-frameworks ⋮ Infinitesimal rigidity for non-Euclidean bar-joint frameworks ⋮ Sparsity-certifying graph decompositions ⋮ Maxwell-Laman counts for bar-joint frameworks in normed spaces

Cites Work

• Linking \((n-2)\)-dimensional panels in \(n\)-space. I: \((k-1,k)\)-graphs and \((k-1,k)\)-frames
• On graphs and rigidity of plane skeletal structures
• Linking (n-2)-dimensional panels in n-space. II: (n-2,2)-frameworks and body and Hinge structures

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