In this paper we take advantage of a recently published algorithm for computing the number of realizations of minimally rigid graphs . 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  realizations for graphs with a given number of vertices. We extend these ideas to rigid frameworks in three dimensions and we derive similar lower bounds, by exploiting data from extensive Gr\"obner basis computations.
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 Gr\"obner basis computations.
R
In this paper
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,
R
for computing the number of realizations of minimally rigid graphs
, which is the fastest available method, although its complexity is still exponential
A
(complex)
R
frameworks
graphs