The generic rigidity of triangulated spheres with blocks and holes

Cruickshank, James and Kitson, Derek and Power, Stephen (2017) The generic rigidity of triangulated spheres with blocks and holes. Journal of Combinatorial Theory, Series B, 122. pp. 550-577. ISSN 0095-8956

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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. Combinatorial characterisations 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.

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, 122, 2017 DOI: 10.1016/j.jctb.2016.08.003
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600/2614
Subjects:
ID Code:
80878
Deposited By:
Deposited On:
12 Aug 2016 08:04
Refereed?:
Yes
Published?:
Published
Last Modified:
09 Aug 2020 03:25