Graph connectivity and universal rigidity of bar frameworks

Abstract

Let $G$ be a graph on $n$ nodes. In this note, we prove that if $G$ is $(r+1)$-vertex connected, $1\le r\le n-2$, then there exists a configuration $p$ in general position in $R^r$ 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 [12,13].

updated version