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On Generic Rigidity in the Plane
Abstract
Let G be a graph. Let us place the points of G in “general” position in the plane and then replace its edges by rigid bars (with flexible joints). We would like to know if the resulting structure is rigid and if not, compute its “degree of freedom”. This problem was solved by Laman [6] (see also [2]). In this note we give some new formulations and a new proof of Laman’s theorem, based on matroid theory, and then apply these to prove the following result: if G is 6-connected, then it will be rigid in the plane. We also construct infinitely many 5-connected graphs which do not have this property.
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Cited by
Submodular functions and convexity
Lovász, L. (1983) · Mathematical Programming The State of the Art · doi:10.1007/978-3-642-68874-4_10 · Cited by 964
Self-citationThe hippocampus as a cognitive graph.
Muller, R. U., Stead, M., & Pach, J. (1996) · The Journal of general physiology · doi:10.1085/jgp.107.6.663 · Cited by 391
Metadata
- Authors
- Lovász, L., & Yemini, Y.
- Venue
- SIAM Journal on Algebraic Discrete Methods
- Published
- 1982-03
- Volume
- 3
- Issue
- 1
- Pages
- 91-98
- ISSN
- 0196-5212 (ISSN-L)
- 2168-345X
- OpenAlex
- W2088062469
- Cited by
- 271
- References
- 0
- FWCI
- 6.00
- Type
- journal article
- Language
- en
- Open access
- closed
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- Lovász, L., & Yemini, Y. (1982). On Generic Rigidity in the Plane. SIAM Journal on Algebraic Discrete Methods. https://doi.org/10.1137/0603009
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