---
tag: SET315RZTV
kind: statement
role: proposition
name: Geiringer–Laman theorem
sources:
  - wikipedia: en:66490111@r1369352305
    locator: Geiringer–Laman theorem
    note: adopted
    mention: wikipedia://en/66490111
    sections: [Statement]
same_as:
  wikidata: Q111955295
  wikipedia: Geiringer–Laman theorem
inventory: [3EVHGCHN0Z]
---

## Statement

The **Geiringer–Laman theorem** gives a combinatorial characterization of generically rigid graphs<sup>*not defined at the linked page*</sup> in $2$-dimensional [[Euclidean space|0XPR1E85W0]], 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.