29 citations · 89 across the 22 of their papers we have counts for
4 papers · 1 filter
From Crossing-Free Graphs on Wheel Sets to Embracing Simplices and Polytopes with Few Vertices
Alexander Pilz, Emo Welzl, Manuel Wettstein
A set of points in general position in the plane is called a wheel set if all points but are extreme. We show that for the purpose of counting crossing…
Extending the centerpoint theorem to multiple points
Alexander Pilz, Patrick Schnider
The centerpoint theorem is a well-known and widely used result in discrete geometry. It states that for any point set of points in , there is a point , not…
Transition Operations over Plane Trees
Torrie L. Nichols, Alexander Pilz, Csaba D. Tóth +1
The operation of transforming one spanning tree into another by replacing an edge has been considered widely, both for general and planar straight-line graphs. For the latter, seve…
A Note on the Flip Distance Problem for Edge-Labeled Triangulations
Alexander Pilz
For both triangulations of point sets and simple polygons, it is known that determining the flip distance between two triangulations is an NP-hard problem. To gain more insight int…