Epsilon-Mnets: Hitting Geometric Set Systems with Subsets

International audience; The existence of Macbeath regions is a classical theorem in convex geometry [13], with recent applications in discrete and computational geometry. In this paper, we initiate the study of Macbeath regions in a combinatorial setting—and not only for the Lebesgue measure as is the case in the classical theorem—and establish near-optimal bounds for several basic geometric set systems.