6 papers
Combinatorics of Bricard's octahedra
Matteo Gallet, Georg Grasegger, Jan Legerský +1
We re-prove the classification of flexible octahedra, obtained by Bricard at the beginning of the XX century, by means of combinatorial objects satisfying some elementary rules. Th…
FlexRiLoG -- A SageMath Package for Motions of Graphs
Georg Grasegger, Jan Legerský
In this paper we present the SageMath package FlexRiLoG (short for flexible and rigid labelings of graphs). Based on recent results the software generates motions of graphs using s…
On the Classification of Motions of Paradoxically Movable Graphs
Georg Grasegger, Jan Legerský, Josef Schicho
Edge lengths of a graph are called flexible if there exist infinitely many non-congruent realizations of the graph in the plane satisfying these edge lengths. It has been shown rec…
On the maximal number of real embeddings of minimally rigid graphs in , and
Evangelos Bartzos, Ioannis Z. Emiris, Jan Legerský +1
Rigidity theory studies the properties of graphs that can have rigid embeddings in a euclidean space or on a sphere and which in addition satisfy certain edge length…
Graphs with Flexible Labelings allowing Injective Realizations
Georg Grasegger, Jan Legerský, Josef Schicho
We consider realizations of a graph in the plane such that the distances between adjacent vertices satisfy the constraints given by an edge labeling. If there are infinitely many s…
On the maximal number of real embeddings of spatial minimally rigid graphs
Evangelos Bartzos, Ioannis Emiris, Jan Legerský +1
The number of embeddings of minimally rigid graphs in is (by definition) finite, modulo rigid transformations, for every generic choice of edge lengths. Even though…