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  • JNcylinderRevised25thFeb2019

    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

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Global rigidity of generic frameworks on the cylinder

Research output: Contribution to journalJournal articlepeer-review

Published
<mark>Journal publication date</mark>1/11/2019
<mark>Journal</mark>Journal of Combinatorial Theory, Series B
Volume139
Number of pages37
Pages (from-to)193-229
Publication StatusPublished
Early online date1/04/19
<mark>Original language</mark>English

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.

Bibliographic note

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