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Lower bounds on the number of realizations of rigid graphs
Abstract : Computing the number of realizations of a minimally rigid graph is a notoriously difficult problem. Towards this goal, for graphs that are minimally rigid in the plane, we take advantage of a recently published algorithm, which is the fastest available method, although its complexity is still exponential. Combining computational results with the theory of constructing new rigid graphs by gluing, we give a new lower bound on the maximal possible number of (complex) realizations for graphs with a given number of vertices. We extend these ideas to rigid graphs in three dimensions and we derive similar lower bounds, by exploiting data from extensive Gröbner basis computations.
Cited literature [26 references]
https://hal.inria.fr/hal-01711441
Contributor : Elias Tsigaridas <>
Submitted on : Saturday, February 17, 2018 - 9:50:34 PM
Last modification on : Tuesday, March 23, 2021 - 9:28:03 AM
Long-term archiving on: : Saturday, May 5, 2018 - 6:25:20 PM
Contributor : Elias Tsigaridas <>
Submitted on : Saturday, February 17, 2018 - 9:50:34 PM
Last modification on : Tuesday, March 23, 2021 - 9:28:03 AM
Long-term archiving on: : Saturday, May 5, 2018 - 6:25:20 PM
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lowerbounds_web.pdf
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