Graph connectivity and universal rigidity of bar frameworks

摘要

Let G be a graph on n nodes. In this note, we prove that if G is (r + 1)-vertex connected, 1 <= r <= n 2, then there exists a configuration pin general position in R' such that the bar framework (G, p) is universally rigid. The proof is constructive, and is based on a theorem by Lovasz et al concerning orthogonal representations and connectivity of graphs Lovasz et al. (0000, 2000). (C) 2016 Elsevier B.V. All rights reserved.