Laman's Theorem

Let a Graph $G$ have exactly $2n-3$ Edges, where $n$ is the number of Vertices in $G$. Then $G$ is ``generically'' Rigid in $\Bbb{R}^2$ Iff $e'\leq 2n'-3$ for every Subgraph of $G$ having $n'$ Vertices and $r'$ Edges.

See also Rigid

References

Laman, G. ``On Graphs and Rigidity of Plane Skeletal Structures.'' J. Engineering Math. 4, 331-340, 1970.