3 papers
cs.CG2022
Well-Separation and Hyperplane Transversals in High Dimensions
Helena Bergold, Daniel Bertschinger, Nicolas Grelier +2
A family of point sets in dimensions is well-separated if the convex hulls of any two disjoint subfamilies can be separated by a hyperplane. Well-separation is a strong ass…
math.CO2019
A Semi-strong Perfect Digraph Theorem
Stephan Dominique Andres, Helena Bergold, Winfried Hochstättler +1
Reed showed that, if two graphs are -isomorphic, then either both are perfect or none of them is. In this note we will derive an analogous result for perfect digraphs.
math.CO2019
On the Geometry of Holmsen's Combinatorial Version of the Colorful Carathéodory
Helena Bergold, Winfried Hochstättler
Carathéodorys Theorem of convex hulls plays an important role in convex geometry. In 1982, Bárány formulated and proved a more general version, called the Colorful Carathéodory. Th…