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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 …
Steven Gortler's user avatar
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. …
Steven Gortler's user avatar
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 …
Steven Gortler's user avatar