A new proof of Laman’s theorem. (English) Zbl 0786.05069
Summary: We give a simple proof for the characterization of generically rigid bar frameworks in the plane.
MSC:
| 05C75 | Structural characterization of families of graphs |
| 52C25 | Rigidity and flexibility of structures (aspects of discrete geometry) |
| 51N20 | Euclidean analytic geometry |
| 05C70 | Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) |
| 05C10 | Planar graphs; geometric and topological aspects of graph theory |
| 05C50 | Graphs and linear algebra (matrices, eigenvalues, etc.) |
| 05C05 | Trees |
References:
| [1] | Laman, G.: On graphs and rigidity of plane skeletal structures, J. Eng. Math.4, 331–340 (1970) · Zbl 0213.51903 · doi:10.1007/BF01534980 |
| [2] | Tay, T.S.: Linking(n – 2)-dimensional panels in n-space II:(n – 1,2)-frameworks and body and hinge structures, Graphs Comb.5, 245–273 (1989) · Zbl 0721.05054 · doi:10.1007/BF01788678 |
| [3] | Tay, T.S.: Linking(n – 2)-dimensional panels in n-space I:(k – 1, k)-graphs and(k – 1,k)- frames, Graphs Comb.7, 289–304 (1991) · Zbl 0759.05083 · doi:10.1007/BF01787636 |
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