Jackson, Bill and Nixon, Anthony Keith (2019) Global rigidity of generic frameworks on the cylinder. Journal of Combinatorial Theory, Series B, 139. pp. 193-229. ISSN 0095-8956
Preview
PDF (JNcylinderRevised25thFeb2019)
JNcylinderRevised25thFeb2019.pdf - Accepted Version
Available under License Creative Commons Attribution-NonCommercial-NoDerivs.
Download (432kB)
JNcylinderRevised25thFeb2019.pdf - Accepted Version
Available under License Creative Commons Attribution-NonCommercial-NoDerivs.
Download (432kB)
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.
Item Type:
Journal Article
Journal or Publication Title:
Journal of Combinatorial Theory, Series B
Additional Information:
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
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600/2607
Subjects:
?? rigidityglobal rigiditycircuitstress matrixframework on a surfacediscrete mathematics and combinatoricscomputational theory and mathematicstheoretical computer science ??
Departments:
ID Code:
131811
Deposited By:
Deposited On:
11 Mar 2019 14:25
Refereed?:
Yes
Published?:
Published
Last Modified:
14 Oct 2024 00:14