On affine rigidity

We study the properties of affine rigidity of a (hyper)graph and prove a variety of fundamental results. First, we show that affine rigidity is a generic property (i.e., only depends on the (hyper)graph, not the particular embedding). Then we prove that a graph is generically neighborhood affinely rigid in d-dimensional Euclidean if it is (d+1)-vertex-connected. We also relate neighborhood affine rigidity of a graph to the universal rigidity of its squared graph. Applications of the theory are discussed.

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Steven J. Gortler, Craig Gotsman, Ligang Liu, Dylan Thurston
• Keywords: Affine Rigidity, CORR 2010, Education, Generic Property, Neighborhood Affine Rigidity