# The discrete yet ubiquitous theorems of Carath'eodory, Helly, Sperner, Tucker, and Tverberg

arXiv: https://arxiv.org/abs/1706.05975 · HTML: https://mlsanity.com/paper/1706.05975/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Jun 2017.

## Built on by (most cited first, 2 of 2)

- [Towards the mathematical foundation of the minimum enclosing ball and related problems](https://mlsanity.com/paper/2402.06629/) (2024)
- [Towards the methodology for solving the minimum enclosing ball and related problems](https://mlsanity.com/paper/2410.11063/) (2024)

## Abstract (arXiv)

We discuss five discrete results: the lemmas of Sperner and Tucker from combinatorial topology and the theorems of Carath'eodory, Helly, and Tverberg from combinatorial geometry. We explore their connections and emphasize their broad impact in application areas such as game theory, graph theory, mathematical optimization, computational geometry, etc.