Laman's theorem

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Theorem (Laman [1]). A graph G=(V,E) is minimally rigid in 2 dimensions if and only if [math]|E|=2|V|-3[/math] and [math]i_G(X) \leq 2|X|-3[/math] for every [math]X \subseteq V[/math] of size at least 2.

References

  1. G. Laman, On graphs and rigidity of plane skeletal structures, DOI link.