14 citations · 73 across the 14 of their papers we have counts for
7 papers · 1 filter
Flexing infinite frameworks with applications to braced Penrose tilings
Sean Dewar, Jan Legerský
A planar framework -- a graph together with a map of its vertices to the plane -- is flexible if it allows a continuous deformation preserving the distances between adjacent vertic…
Bracing frameworks consisting of parallelograms
Georg Grasegger, Jan Legerský
A rectangle in the plane can be continuously deformed preserving its edge lengths, but adding a diagonal brace prevents such a deformation. Bolker and Crapo characterized combinato…
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…
Flexible placements of graphs with rotational symmetry
Sean Dewar, Georg Grasegger, Jan Legerský
We study the existence of an -fold rotationally symmetric placement of a symmetric graph in the plane allowing a continuous deformation that preserves the symmetry and the dista…
On the existence of paradoxical motions of generically rigid graphs on the sphere
Matteo Gallet, Georg Grasegger, Jan Legerský +1
We interpret realizations of a graph on the sphere up to rotations as elements of a moduli space of curves of genus zero. We focus on those graphs that admit an assignment of edge…
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…
Graphs with Flexible Labelings
Georg Grasegger, Jan Legerský, Josef Schicho
For a flexible labeling of a graph, it is possible to construct infinitely many non-equivalent realizations keeping the distances of connected points constant. We give a combinator…