3 papers
math.CO2026
On the Largest Convexity Number of Co-Finite Sets in the Plane
Chaya Keller, Micha A. Perles
The convexity number of a set is the minimum number of convex subsets required to cover it. We study the following question: what is the largest possible c…
math.CO2025
An -Theorem for -Transversals
Chaya Keller, Micha A. Perles
A family of sets satisfies the -property if among every members of , some can be pierced by a single point. The celebrated -theorem…
math.CO2025
Complements of finite unions of convex sets
Chaya Keller, Micha A. Perles
Finite unions of convex sets are a central object of study in discrete and computational geometry. In this paper we initiate a systematic study of complements of such unions -- i.e…