3 citations
- Center for Massive Data AlgorithmicsDK4 papers
- Centre National de la Recherche ScientifiqueFR4 papers
- Institut national de recherche en sciences et technologies du numériqueFR4 papers
- Korea Advanced Institute of Science and TechnologyKR4 papers
- Laboratoire Lorrain de Recherche en Informatique et ses ApplicationsFR4 papers
- National Institute for Mathematical SciencesKR4 papers
- Université de LorraineFR4 papers
4 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…