2 papers
math.CO2025
Helly-type theorems for monotone properties of boxes
Nóra Frankl, Attila Jung
We present a unified approach to prove Helly-type theorems for monotone properties of boxes, such as having large volume or containing points from a given set. As a corollary, we o…
math.CO2024
The Quantitative Fractional Helly theorem
Nóra Frankl, Attila Jung, István Tomon
Two celebrated extensions of Helly's theorem are the Fractional Helly theorem of Katchalski and Liu (1979) and the Quantitative Volume theorem of Bárány, Katchalski, and Pach (19…