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Generically globally rigid graphs have generic universally rigid frameworks

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Connelly_2018_Generically_globally_Combinatorica_AAM.pdf (546.5Kb)
Date
22/03/2020
Author
Connelly, Robert
Gortler, Steven
Theran, Louis Simon
Keywords
QA Mathematics
T-NDAS
BDC
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Abstract
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
DOI
https://doi.org/10.1007/s00493-018-3694-4
ISSN
0209-9683
Type
Journal article
Rights
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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  • University of St Andrews Research
URL
http://arxiv.org/abs/1604.07475
URI
http://hdl.handle.net/10023/21677

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