Rights statement: This is the author’s version of a work that was accepted for publication in Journal of Combinatorial Theory, Series B. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Combinatorial Theory, Series B, 139, 2019 DOI: 10.1016/j.jctb.2019.03.002
Accepted author manuscript, 422 KB, PDF document
Available under license: CC BY-NC-ND: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
Final published version
Research output: Contribution to Journal/Magazine › Journal article › peer-review
| <mark>Journal publication date</mark> | 1/11/2019 |
|---|---|
| <mark>Journal</mark> | Journal of Combinatorial Theory, Series B |
| Volume | 139 |
| Number of pages | 37 |
| Pages (from-to) | 193-229 |
| Publication Status | Published |
| Early online date | 1/04/19 |
| <mark>Original language</mark> | English |
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.