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arXiv · 1710.08237

Lower bounds on the number of realizations of rigid graphs

Georg Grasegger·Christoph Koutschan·Elias Tsigaridas
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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.

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Georg Grasegger, Christoph Koutschan, Elias Tsigaridas. 2018-04-11. Lower bounds on the number of realizations of rigid graphs. https://doi.org/10.1080/10586458.2018.1437851

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