Quantitative Fractional Helly and $(p,q)$-Theorems
Metric Geometry
2021-01-25 v2 Combinatorics
Abstract
We consider quantitative versions of Helly-type questions, that is, instead of finding a point in the intersection, we bound the volume of the intersection. Our first main geometric result is a quantitative version of the Fractional Helly Theorem of Katchalski and Liu, the second one is a quantitative version of the -Theorem of Alon and Kleitman.
Cite
@article{arxiv.2012.08964,
title = {Quantitative Fractional Helly and $(p,q)$-Theorems},
author = {Attila Jung and Márton Naszódi},
journal= {arXiv preprint arXiv:2012.08964},
year = {2021}
}
Comments
11 pages