Rigidity of Graph Joins and Hendrickson's Conjecture

Details Rigidity of Graph Joins and Hendrickson's Conjecture Rigidity of Graph Joins and Hendrickson's Conjecture

2010-11-14

arxiv.org/abs/1011.3208v2

Mathematics

Metric Geometry

Scientific paper

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 $\R^5$ and above to Hendrickson's conjecture on generic global rigidity.

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