19 citations · 74 across the 43 of their papers we have counts for
8 papers · 1 filter
Blocking Delaunay Triangulations from the Exterior
Oswin Aichholzer, Thomas Hackl, Maarten Löffler +4
Given two distinct point sets and in the plane, we say that \emph{blocks} if no two points of are adjacent in any Delaunay triangulation of . Aichholze…
No Selection Lemma for Empty Triangles
Ruy Fabila-Monroy, Carlos Hidalgo-Toscano, Daniel Perz +1
Let be a set of points in general position in the plane. The Second Selection Lemma states that for any family of triangles spanned by , there exists a point of…
Shooting Stars in Simple Drawings of
Oswin Aichholzer, Alfredo García, Irene Parada +2
Simple drawings are drawings of graphs in which two edges have at most one common point (either a common endpoint, or a proper crossing). It has been an open question whether every…
Compatible Spanning Trees in Simple Drawings of
Oswin Aichholzer, Kristin Knorr, Wolfgang Mulzer +6
For a simple drawing of the complete graph , two (plane) subdrawings are compatible if their union is plane. Let be the set of all plane spanning trees on…
Empty Triangles in Generalized Twisted Drawings of
Alfredo García, Javier Tejel, Birgit Vogtenhuber +1
Simple drawings are drawings of graphs in the plane or on the sphere such that vertices are distinct points, edges are Jordan arcs connecting their endpoints, and edges intersect a…
Coloring circle arrangements: New -chromatic planar graphs
Man-Kwun Chiu, Stefan Felsner, Manfred Scheucher +3
Felsner, Hurtado, Noy and Streinu (2000) conjectured that arrangement graphs of simple great-circle arrangements have chromatic number at most . Motivated by this conjecture, we…
Twisted Ways to Find Plane Structures in Simple Drawings of Complete Graphs
Oswin Aichholzer, Alfredo García, Javier Tejel +2
Simple drawings are drawings of graphs in which the edges are Jordan arcs and each pair of edges share at most one point (a proper crossing or a common endpoint). We introduce a sp…
Flipping Plane Spanning Paths
Oswin Aichholzer, Kristin Knorr, Wolfgang Mulzer +3
Let be a planar point set in general position, and let be the set of all plane straight-line paths with vertex set . A flip on a path …