Helly-type Problems

2021/08/19 by Bárány, Imre, Kalai, Gil · 6 citations
#52A20 #52A35 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2108.08804

Abstract

In this paper, we present a variety of problems in the interface between combinatorics and geometry around the theorems of Helly, Radon, Carathéodory, and Tverberg. Through these problems we describe the fascinating area of Helly-type theorems, and explain some of its main themes and goals.

Cited by

• Quantitative selection theorems
• Colourful Carathéodory's Theorem plus a constraint
• Strong invariants and Tverberg numbers in convexity spaces
• A simple proof of a (p,2)-theorem for non-piercing regions
• Unimodality for Radon partitions of random vectors
• Extended VC-dimension, and Radon and Tverberg type theorems for unions of convex sets

Related

• Helly's Theorem: New Variations and Applications
• A Helly-type problem
• Quantitative Helly-type Theorems via Hypergraph Chains
• Carathéodory, Helly and the others in the max-plus world
• The discrete yet ubiquitous theorems of Carath 'eodory, Helly, Sperner,\n Tucker, and Tverberg