Global rigidity of generic frameworks on the cylinder

DOI10.1016/J.JCTB.2019.03.002zbMATH Open1428.05076arXiv1610.07755OpenAlexW2964023517WikidataQ128141091 ScholiaQ128141091MaRDI QIDQ2338637

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Publication date: 21 November 2019

Published in: (Search for Journal in Brave)

Abstract: 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.

Full work available at URL: https://arxiv.org/abs/1610.07755

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