Global rigidity of generic frameworks on the cylinder

摘要

We show that a generic framework (G, p) on the cylinder is globally rigid if and only if G is a complete graph on at most four vertices or G is both redundantly rigid and 2-connected. To prove the theorem we also derive a new recursive construction of circuits in the simple (2, 2)-sparse matroid, and a characterisation of rigidity for generic frameworks on the cylinder when a single designated vertex is allowed to move off the cylinder. (C) 2019 Elsevier Inc. All rights reserved.