Tverberg partitions as weak epsilon-nets

Abstract

We prove a Tverberg-type theorem using the probabilistic method. Given $\epsilon >0$, we find the smallest number of partitions of a set $X$ in $R^d$ into $r$ parts needed in order to induce at least one Tverberg partition on every subset of $X$ with at least $\epsilon |X|$ elements. This generalizes known results about Tverberg's theorem with tolerance.

14 pages

References in corpus (3)

• Optimal bounds for a colorful Tverberg--Vrecica type problem
• Lower bounds for weak epsilon-nets and stair-convexity
• Robust Tverberg and colorful Carathéodory results via random choice