Rigid cylindrical frameworks with two coincident points

Bill Jackson, Viktória Kaszanitzky, Anthony Nixon

Published in:
Graphs and Combinatorics volume 35, pages141–168(2019). DOI link


We develop a rigidity theory for frameworks in $\mathbb{R}^3$ which have two coincident points but are otherwise generic and only infinitesimal motions which are tangential to a family of cylinders induced by the realisation are considered. We then apply our results to show that vertex splitting, under the additional assumption that the new edge is redundant, preserves the property of being generically globally rigid on families of concentric cylinders.

Bibtex entry:

AUTHOR = {Jackson, Bill and Kaszanitzky, Vikt{\'o}ria and Nixon, Anthony},
TITLE = {Rigid cylindrical frameworks with two coincident points},
NOTE= {{\tt}},
INSTITUTION = {Egerv{\'a}ry Research Group, Budapest},
YEAR = {2016},
NUMBER = {TR-2016-05}

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