4 papers · 1 filter
Diameter and Length of Metric Graphs
Hee-Kap Ahn, Sergio Cabello, Otfried Cheong +2
A metric graph is a metric space obtained from a finite collection of intervals whose endpoints are identified in groups. It can also be seen as a finite, edge-weighted graph where…
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…