Author: Brigitte Servatius
Reference: SIAM J. Disc. Math. \vol{2}, 4, 582--589, 1989.
Abstract: We consider the 2-dimensional generic rigidity matroid $R(G)$ of a graph $G$. The notions of vertex and edge birigidity are introduced. We prove that vertex birigidity of $G$ implies the connectivity of R(G) and that the connectivity of $R(G)$ implies the edge birigidity of $G$. These implications are not equivalences. A class of minimal vertex birigid graphs is exhibited and used to show that $R(G)$ is not representable over any finite field.