76 citations · 542 across the 72 of their papers we have counts for
12 papers · 1 filter
Irreducible components of sets of points in the plane that satisfy distance conditions
Niels Lubbes, Mehdi Makhul, Josef Schicho +1
For a given graph whose edges are labeled with general real numbers, we consider the set of functions from the vertex set into the Euclidean plane such that the distance between th…
Calligraphs and sphere realizations
Matteo Gallet, Georg Grasegger, Niels Lubbes +1
We introduce a recursive procedure for computing the number of realizations of a minimally rigid graph on the sphere up to rotations. We accomplish this by combining two ingredient…
On Galois groups of type-1 minimally rigid graphs
Mehdi Makhul, Josef Schicho, Audie Warren
For every graph that is mimimally rigid in the plane, its Galois group is defined as the Galois group generated by the coordinates of its planar realizations, assuming that the edg…
Five Equivalent Representations of a Phylogenetic Tree
Jiayue Qi, Josef Schicho
A phylogenetic tree is a tree with a fixed set of leaves that has no vertices of degree two. In this paper, we axiomatically define four other discrete structures on the set of lea…
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 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…
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…
Probabilities of incidence between lines and a plane curve over finite fields
Mehdi Makhul, Josef Schicho, Matteo Gallet
We study the probability for a random line to intersect a given plane curve, defined over a finite field, in a given number of points defined over the same field. In particular, we…
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…
On sets defining few ordinary circles
Aaron Lin, Mehdi Makhul, Hossein Nassajian Mojarrad +3
An ordinary circle of a set of points in the plane is defined as a circle that contains exactly three points of . We show that if is not contained in a line or a cir…
Lattice polygons and the number 2i+7
Christian Haase, Josef Schicho
In this note we classify all triples (a,b,i) such that there is a convex lattice polygon P with area a, and b respectively i lattice points on the boundary respectively in the inte…