New Classes of Counterexamples to Hendrickson’s Global Rigidity Conjecture

We examine the generic local and global rigidity of various graphs in ℝ d . Bruce Hendrickson showed that some necessary conditions for generic global rigidity are ( d +1)-connectedness and generic redundant rigidity, and hypothesized that they were sufficient in all dimensions. We analyze two classes of graphs that satisfy Hendrickson’s conditions for generic global rigidity, yet fail to be generically globally rigid. We find a large family of bipartite graphs for d >3, and we define a construction that generates infinitely many graphs in ℝ 5 . Finally, we state some conjectures for further exploration.