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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Final published version
Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
}
TY - JOUR
T1 - Global rigidity of generic frameworks on the cylinder
AU - Jackson, Bill
AU - Nixon, Anthony Keith
N1 - 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
PY - 2019/11/1
Y1 - 2019/11/1
N2 - 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.
AB - 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.
KW - Rigidity
KW - Global rigidity
KW - Circuit
KW - Stress matrix
KW - Framework on a surface
U2 - 10.1016/j.jctb.2019.03.002
DO - 10.1016/j.jctb.2019.03.002
M3 - Journal article
VL - 139
SP - 193
EP - 229
JO - Journal of Combinatorial Theory, Series B
JF - Journal of Combinatorial Theory, Series B
SN - 0095-8956
ER -