4 papers
On rigidity properties of unit-distance graphs
Sean Dewar, Georg Grasegger, Alison La Porta +2
A unit-distance graph is a graph which admits a realisation in Euclidean space in which every edge has unit length. Imposing further geometric conditions on the non-edges gives a f…
Learning Minimally Rigid Graphs with High Realization Counts
Oleksandr Slyvka, Jan Rubeš, Rodrigo Alves +1
For minimally rigid graphs, the same edge-length data can admit multiple realizations (up to translations and rotations). Finding graphs with exceptionally many realizations is an…
PyRigi -- a general-purpose Python package for the rigidity and flexibility of bar-and-joint frameworks
Matteo Gallet, Georg Grasegger, Matthias Himmelmann +1
We present PyRigi, a novel Python package designed to study the rigidity properties of graphs and frameworks. Among many other capabilities, PyRigi can determine whether a graph ad…
Constructing reflection-symmetric flexible realisations of graphs
Sean Dewar, Georg Grasegger, Jan Legerský
We study reflection-symmetric realisations of symmetric graphs in the plane that allow a continuous symmetry and edge-length preserving deformation. To do so, we identify a necessa…