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  • The generic rigidity of triangulated spheres with blocks and holes

    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, 122, 2017 DOI: 10.1016/j.jctb.2016.08.003

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The generic rigidity of triangulated spheres with blocks and holes

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The generic rigidity of triangulated spheres with blocks and holes. / Cruickshank, James; Kitson, Derek; Power, Stephen.

In: Journal of Combinatorial Theory, Series B, Vol. 122, 01.2017, p. 550-577.

Research output: Contribution to journalJournal articlepeer-review

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Cruickshank, J, Kitson, D & Power, S 2017, 'The generic rigidity of triangulated spheres with blocks and holes', Journal of Combinatorial Theory, Series B, vol. 122, pp. 550-577. https://doi.org/10.1016/j.jctb.2016.08.003

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Cruickshank, James ; Kitson, Derek ; Power, Stephen. / The generic rigidity of triangulated spheres with blocks and holes. In: Journal of Combinatorial Theory, Series B. 2017 ; Vol. 122. pp. 550-577.

Bibtex

@article{71559300af284933ae86b9be92aea01c,
title = "The generic rigidity of triangulated spheres with blocks and holes",
abstract = "A simple graph G = (V,E) is 3-rigid if its generic bar-joint frameworks in R^3 are infinitesimally rigid. Block and hole graphs are derived from triangulated spheres by the removal of edges and the addition of minimally rigid subgraphs, known as blocks, in some of the resulting holes. Combinatorialcharacterisations of minimal 3-rigidity are obtained for these graphs in the case of a single block and finitely many holes or a single hole and finitely many blocks. These results confirm a conjecture of Whiteley from 1988 and special cases of a stronger conjecture of Finbow-Singh and Whiteley from 2013.",
keywords = "Infinitesimal rigidity, Vertex splitting, Bar-joint framework, Combinatorial rigidity",
author = "James Cruickshank and Derek Kitson and Stephen Power",
note = "This is the author{\textquoteright}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, 122, 2017 DOI: 10.1016/j.jctb.2016.08.003",
year = "2017",
month = jan,
doi = "10.1016/j.jctb.2016.08.003",
language = "English",
volume = "122",
pages = "550--577",
journal = "Journal of Combinatorial Theory, Series B",
issn = "0095-8956",
publisher = "Academic Press Inc.",

}

RIS

TY - JOUR

T1 - The generic rigidity of triangulated spheres with blocks and holes

AU - Cruickshank, James

AU - Kitson, Derek

AU - Power, Stephen

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, 122, 2017 DOI: 10.1016/j.jctb.2016.08.003

PY - 2017/1

Y1 - 2017/1

N2 - A simple graph G = (V,E) is 3-rigid if its generic bar-joint frameworks in R^3 are infinitesimally rigid. Block and hole graphs are derived from triangulated spheres by the removal of edges and the addition of minimally rigid subgraphs, known as blocks, in some of the resulting holes. Combinatorialcharacterisations of minimal 3-rigidity are obtained for these graphs in the case of a single block and finitely many holes or a single hole and finitely many blocks. These results confirm a conjecture of Whiteley from 1988 and special cases of a stronger conjecture of Finbow-Singh and Whiteley from 2013.

AB - A simple graph G = (V,E) is 3-rigid if its generic bar-joint frameworks in R^3 are infinitesimally rigid. Block and hole graphs are derived from triangulated spheres by the removal of edges and the addition of minimally rigid subgraphs, known as blocks, in some of the resulting holes. Combinatorialcharacterisations of minimal 3-rigidity are obtained for these graphs in the case of a single block and finitely many holes or a single hole and finitely many blocks. These results confirm a conjecture of Whiteley from 1988 and special cases of a stronger conjecture of Finbow-Singh and Whiteley from 2013.

KW - Infinitesimal rigidity

KW - Vertex splitting

KW - Bar-joint framework

KW - Combinatorial rigidity

U2 - 10.1016/j.jctb.2016.08.003

DO - 10.1016/j.jctb.2016.08.003

M3 - Journal article

VL - 122

SP - 550

EP - 577

JO - Journal of Combinatorial Theory, Series B

JF - Journal of Combinatorial Theory, Series B

SN - 0095-8956

ER -