### 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 2005 |

### Fingerprint

### Keywords

- Graph
- Realization
- Rigidity

### ASJC Scopus subject areas

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

### Cite this

*Computational Geometry: Theory and Applications*,

*32*(3), 216-222. https://doi.org/10.1016/j.comgeo.2005.04.001

**Rigid realizations of graphs on small grids.** / Fekete, Zsolt; Jordán, T.

Research output: Contribution to journal › Article

*Computational Geometry: Theory and Applications*, vol. 32, no. 3, pp. 216-222. https://doi.org/10.1016/j.comgeo.2005.04.001

}

TY - JOUR

T1 - Rigid realizations of graphs on small grids

AU - Fekete, Zsolt

AU - Jordán, T.

PY - 2005/11

Y1 - 2005/11

N2 - 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.

AB - 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.

KW - Graph

KW - Realization

KW - Rigidity

UR - http://www.scopus.com/inward/record.url?scp=84867951749&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84867951749&partnerID=8YFLogxK

U2 - 10.1016/j.comgeo.2005.04.001

DO - 10.1016/j.comgeo.2005.04.001

M3 - Article

VL - 32

SP - 216

EP - 222

JO - Computational Geometry: Theory and Applications

JF - Computational Geometry: Theory and Applications

SN - 0925-7721

IS - 3

ER -