English

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 (p,q)(p,q)-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

R2 v1 2026-06-23T21:01:05.487Z