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
Accepted author manuscript, 131 KB, PDF document
Available under license: CC BY-NC-ND: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
Final published version
Licence: CC BY: Creative Commons Attribution 4.0 International License
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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 Journal/Magazine › Journal article › peer-review
}
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 -