Geiringer–Laman theorem

Statement

The Geiringer–Laman theorem gives a combinatorial characterization of generically rigid graphs^{not defined at the linked page} in $2$-dimensional Euclidean space, with respect to bar-joint frameworks. This theorem was first proved by Hilda Pollaczek-Geiringer in 1927, and later by Gerard Laman in 1970. An efficient algorithm called the pebble game is used to identify this class of graphs. This theorem has been the inspiration for many Geiringer-Laman type results for other types of frameworks with generalized pebble games.