### Abstract

A framework (G,p) is a straight line realization of a graph G=(V,E) in R ^{2}, given by a map pV→R ^{2}. We prove that if (G,p) is an infinitesimally rigid framework then there is an infinitesimally rigid framework (G,q) for which the points q(v), v∈V(G), are distinct points of the k×k grid, where k=⌈√|V|-1⌉+9. We also show that such a framework on G can be constructed in O(| ^{V|3}) time.

Original language | English |
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Pages (from-to) | 216-222 |

Number of pages | 7 |

Journal | Computational Geometry: Theory and Applications |

Volume | 32 |

Issue number | 3 |

DOIs | |

Publication status | Published - Nov 1 2005 |

### Keywords

- Graph
- Realization
- Rigidity

### ASJC Scopus subject areas

- Computer Science Applications
- Geometry and Topology
- Control and Optimization
- Computational Theory and Mathematics
- Computational Mathematics

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## Cite this

Fekete, Z., & Jordán, T. (2005). Rigid realizations of graphs on small grids.

*Computational Geometry: Theory and Applications*,*32*(3), 216-222. https://doi.org/10.1016/j.comgeo.2005.04.001