Rigid realizations of graphs on small grids

Authors:
Zsolt Fekete;Tibor Jordán
Affiliations:
Department of Operations Research, Eötvös University, Pázmány sétány 1/C, 1117 Budapest, Hungary and Communication Networks Laboratory, Pázmány sét ...;Department of Operations Research, Eötvös University, Pázmány sétány 1/C, 1117 Budapest, Hungary
Venue:
Computational Geometry: Theory and Applications
Year:
2005

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Abstract

A framework (G,p) is a straight line realization of a graph G=(V,E) in R^2, given by a map p:V-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 kxk grid, where k=@?|V|-1@?+9. We also show that such a framework on G can be constructed in O(|V|^3) time.