Generically globally rigid graphs have generic universally rigid frameworks
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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.
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
Copyright © 2020 János Bolyai Mathematical Society and Springer-Verlag Berlin Heidelberg. This work has been made available online in accordance with publisher policies or with permission. Permission for further reuse of this content should be sought from the publisher or the rights holder. This is the author created accepted manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.1007/s00493-018-3694-4.
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