\varepsilon $e Mnets: Hitting Geometric Set Systems with Subsets
The existence of Macbeath regions is a classical theorem in convex geometry (Macbeath in Ann Math 56:269 293, 1952) with recent applications in discrete and computational geometry. In this paper, we initiate the study of Macbeath regions in a combinatorial setting and establish near optimal bounds for several basic geometric set systems.
Discret. Comput. Geom.