English

Universal rigidity on the line, point order

Combinatorics 2021-04-06 v1 Algebraic Geometry Metric Geometry

Abstract

We show that universal rigidity of a generic bar and joint framework (G,p) in the line depends on more than the ordering of the vertices. In particular, we construct examples of one-dimensional generic frameworks with the same graph and ordering of the vertices, such that one is universally rigid and one is not. This answers, in the negative, a question of Jordan and Nguyen.

Keywords

Cite

@article{arxiv.2104.01892,
  title  = {Universal rigidity on the line, point order},
  author = {Bryan Chen and Robert Connelly and Anthony Nixon and Louis Theran},
  journal= {arXiv preprint arXiv:2104.01892},
  year   = {2021}
}

Comments

9 pages, 6 figures

R2 v1 2026-06-24T00:51:16.386Z