One brick at a time: a survey of inductive constructions in rigidity theory
Abstract
We present a survey of results concerning the use of inductive constructions to study the rigidity of frameworks. By inductive constructions we mean simple graph moves which can be shown to preserve the rigidity of the corresponding framework. We describe a number of cases in which characterisations of rigidity were proved by inductive constructions. That is, by identifying recursive operations that preserved rigidity and proving that these operations were sufficient to generate all such frameworks. We also outline the use of inductive constructions in some recent areas of particularly active interest, namely symmetric and periodic frameworks, frameworks on surfaces, and bodybar frameworks. We summarize the key outstanding open problems related to inductions.
 Publication:

arXiv eprints
 Pub Date:
 March 2012
 arXiv:
 arXiv:1203.6623
 Bibcode:
 2012arXiv1203.6623N
 Keywords:

 Mathematics  Metric Geometry;
 Mathematics  Combinatorics;
 52C25
 EPrint:
 24 pages, 12 figures, final version