An upper bound on Euclidean embeddings of rigid graphs with 8 vertices
Computational Geometry
2014-10-24 v2
Abstract
A graph is called (generically) rigid in R^d if, for any choice of sufficiently generic edge lengths, it can be embedded in R^d in a finite number of distinct ways, modulo rigid transformations. Here, we deal with the problem of determining the maximum number of planar Euclidean embeddings of minimally rigid graphs with 8 vertices, because this is the smallest unknown case in the plane.
Keywords
Cite
@article{arxiv.1204.6527,
title = {An upper bound on Euclidean embeddings of rigid graphs with 8 vertices},
author = {Stylianos C. Despotakis and Ioannis Z. Emiris},
journal= {arXiv preprint arXiv:1204.6527},
year = {2014}
}
Comments
This paper has been withdrawn by the authors because there was a bug in the code used to produce the sub-systems in Section 4. More specifically some of the sub-systems don't satisfy the Laman property. For an update on this problem, see arXiv:1402.1484