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Journal Articles Experimental Mathematics Year : 2018

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.
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Dates and versions

hal-01711441 , version 1 (17-02-2018)

Identifiers

  • HAL Id : hal-01711441 , version 1

Cite

Georg Grasegger, Christoph Koutschan, Elias Tsigaridas. Lower bounds on the number of realizations of rigid graphs. Experimental Mathematics, In press, pp.1-22. ⟨hal-01711441⟩
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