Rigidity of Graph Joins and Hendrickson's Conjecture
Abstract
Whiteley 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 5 and above to Hendrickson's conjecture on generic global rigidity.
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