5 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…
Counting realizations of Laman graphs on the sphere
Matteo Gallet, Georg Grasegger, Josef Schicho
We present an algorithm that computes the number of realizations of a Laman graph on a sphere for a general choice of the angles between the vertices. The algorithm is based on the…
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…