Generically globally rigid graphs have generic universally rigid frameworks
Date
22/03/2020Metadata
Show full item recordAbstract
We show that any graph that is generically globally rigid in ℝd has a realization in ℝd both generic and universally rigid. It also must have a realization in ℝd that is both infinitesimally rigid and universally rigid. This also implies that the graph also must have a realization in ℝd that is both infinitesimally rigid and universally rigid; such a realization serves as a certificate of generic global rigidity. Our approach involves an algorithm by Lovász, Saks and Schrijver that, for a sufficiently connected graph, constructs a general position orthogonal representation of the vertices, and a result of Alfakih that shows how this representation leads to a stress matrix and a universally rigid framework of the graph.
Citation
Connelly , R , Gortler , S & Theran , L S 2020 , ' Generically globally rigid graphs have generic universally rigid frameworks ' , Combinatorica , vol. 40 , pp. 1-37 . https://doi.org/10.1007/s00493-018-3694-4
Publication
Combinatorica
Status
Peer reviewed
ISSN
0209-9683Type
Journal article
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