A fractional Helly theorem for boxes

I. Bárány, F. Fodor, A. Martínez-Pérez +3

Let $\mathcal{F}$ be a family of $n$ axis-parallel boxes in ${\mathbb{R}}^d$ and $\alpha \in (1-1/d,1]$ a real number. There exists a real number $\beta (\alpha )>0$ such that if there are $α{n\choos…