Rigid realizations of graphs on small grids

Zsolt Fekete, T. Jordán

Research output: Contribution to journalArticle

2 Citations (Scopus)

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 languageEnglish
Pages (from-to)216-222
Number of pages7
JournalComputational Geometry: Theory and Applications
Volume32
Issue number3
DOIs
Publication statusPublished - Nov 2005

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Grid
Graph in graph theory
Straight Line
Distinct
Framework

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

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

In: Computational Geometry: Theory and Applications, Vol. 32, No. 3, 11.2005, p. 216-222.

Research output: Contribution to journalArticle

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