Graph connectivity and universal rigidity of bar frameworks

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 p in general position in Rr such that the bar framework (G,p) is universally rigid. The proof is constructive, and is based on a theorem by Lovász et al concerning orthogonal representations and connectivity of graphs Lovász et al. (0000, 2000).