Extended VC-dimension, and Radon and Tverberg type theorems for unions of convex sets
Abstract
We define and study an extension of the notion of the VC-dimension of a hypergraph and apply it to establish a Tverberg type theorem for unions of convex sets. We also prove a new Radon type theorem for unions of convex sets and settle a well-known open problem posed by Kalai in the 1970s.
Fields of Study & Subjects
Digital Image Processing Techniques
Computational Geometry and Mesh Generation
Advanced Banach Space Theory
Publication details
- Journal / source
- Society for Industrial and Applied Mathematics eBooks
- Pages
- 6223–6232
- Publication date
- 1 January 2026
- Language
- EN