A necessary condition for generic rigidity of bar-and-joint frameworks in $d$-space

Bill Jackson, Hakan Guler

A graph $G=(V,E)$ is $d$-sparse if each subset $X\subseteq V$ with $|X|\ge d$ induces at most $d|X|-\left(\genfrac{}{}{0ex}{}{d+1}{2}\right)$ edges in $G$. Maxwell showed in 1864 that a necessary condit…