3 papers
cs.CG2018
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…
cs.CG2016
Counting and Enumerating Crossing-free Geometric Graphs
Manuel Wettstein
We describe a framework for counting and enumerating various types of crossing-free geometric graphs on a planar point set. The framework generalizes ideas of Alvarez and Seidel, w…
cs.CG2016
Trapezoidal Diagrams, Upward Triangulations, and Prime Catalan Numbers
Manuel Wettstein
The d-dimensional Catalan numbers form a well-known sequence of numbers which count balanced bracket expressions over an alphabet of size d. In this paper, we introduce and study w…