4 citations · 4 across the 3 of their papers we have counts for
7 papers
A Note on the Faces of the Dual Koch Arrangement
Bernd Gärtner, Manuel Wettstein
We analyze the faces of the dual Koch arrangement, which is the arrangement of lines obtained by projective duality from the Koch chain . In particular, we show that…
Chains, Koch Chains, and Point Sets with many Triangulations
Daniel Rutschmann, Manuel Wettstein
We introduce the abstract notion of a chain, which is a sequence of points in the plane, ordered by -coordinates, so that the edge between any two consecutive points is unav…
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…
Arc diagrams, flip distances, and Hamiltonian triangulations
Jean Cardinal, Michael Hoffmann, Vincent Kusters +2
We show that every triangulation (maximal planar graph) on vertices can be flipped into a Hamiltonian triangulation using a sequence of less than combinatorial edge…
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…
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…
An Optimal Algorithm for Reconstructing Point Set Order Types from Radial Orderings
Oswin Aichholzer, Vincent Kusters, Wolfgang Mulzer +2
Let be a set of labeled points in the plane. The radial system of describes, for each , the order in which a ray that rotates around encounters the points i…