Universal rigidity on the line, point order

Authors: Robert Connelly, Steven J. Gortler, and Louis Theran
Preprint: 2104.01892, 2021
Full text: arXiv

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.