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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

Research output: Contribution to journalJournal articlepeer-review

Published
<mark>Journal publication date</mark>01/2017
<mark>Journal</mark>Journal of Combinatorial Theory, Series B
Volume122
Number of pages28
Pages (from-to)550-577
Publication StatusPublished
Early online date1/09/16
<mark>Original language</mark>English

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.

Bibliographic note

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