32 citations
- Aarhus UniversityDK11 papers
- Korea Advanced Institute of Science and TechnologyKR5 papers
- Centre National de la Recherche ScientifiqueFR4 papers
- GAMBLE: Géométrie, Algorithmes et Modèles Bien au-delà du Linéaire et de l'EuclidienFR4 papers
- Institut national de recherche en sciences et technologies du numériqueFR4 papers
- Laboratoire Lorrain de Recherche en Informatique et ses ApplicationsFR4 papers
- National Institute for Mathematical SciencesKR4 papers
- Université de LorraineFR4 papers
- Aristotle University of ThessalonikiGR2 papers
- Chinese University of Hong KongHK2 papers
- Danish National Research FoundationDK2 papers
- Hong Kong University of Science and TechnologyHK2 papers
19 papers
The Topology of the set of line Transversals
Otfried Cheong, Xavier Goaoc, Andreas F. Holmsen
We prove that for any set of pairwise disjoint open convex sets in , the connected components of the set of lines intersecting every member of are co…
A colorful Goodman-Pollack-Wenger theorem
Andreas F. Holmsen
Hadwiger's transversal theorem gives necessary and sufficient conditions for the existence of a line transversal to a family of pairwise disjoint convex sets in the plane. These co…
No weak epsilon nets for lines and convex sets in space
Otfried Cheong, Xavier Goaoc, Andreas F. Holmsen
We prove that there exist no weak -nets of constant size for lines and convex sets in .
On a transversal theorem of Montejano and Karasev
Andreas F. Holmsen
We give a new proof of a theorem of Montejano and Karasev regarding -dimensional transversals to small families of convex sets. While their proof uses technical algebraic and to…
Computing the Expected Value and Variance of Geometric Measures
Frank Staals, Constantinos Tsirogiannis
Let P be a set of points in R^d, and let M be a function that maps any subset of P to a positive real number. We examine the problem of computing the exact mean and variance of M w…
How to morph planar graph drawings
Soroush Alamdari, Patrizio Angelini, Fidel Barrera-Cruz +10
Given an -vertex graph and two straight-line planar drawings of the graph that have the same faces and the same outer face, we show that there is a morph (i.e., a continuous tra…