Rigidity of Graph Joins and Hendrickson's Conjecture
arXiv:1011.3208
Abstract
Whiteley \cite{wh} gives a complete characterization of the infinitesimal flexes of complete bipartite frameworks. Our work generalizes a specific infinitesimal flex to include joined graphs, a family of graphs that contain the complete bipartite graphs. We use this characterization to identify new families of counterexamples, including infinite families, in and above to Hendrickson's conjecture on generic global rigidity.