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5
votes
Accepted
Does there exist a 3-connected, chordal graph which is not globally rigid?
(Note that you need to be a bit careful with universal rigidity as there are graphs that have some generic frameworks that are universally rigid in $E^2$, and other generic frameworks that are not universally …
3
votes
Is the following two-dimensional graph likely to be globally rigid?
The main ones to avoid are places where the rigidity matrix, or the stress matrix has a "less than maximal rank". … At such points, global rigidity can be lost. Avoiding such places is needed in Connelly's sufficiency proof. …
3
votes
Is the following two-dimensional graph likely to be globally rigid?
Note that condions 1 and 2 define a so called "unit-disk" graph. Even in this case, finding an embedding from distances is still NP-HARD.
(see "A Theory of Network Localization" by Aspnes et al.) Thou …