2 problems

Let $A,B$ be two multisets of axis-parallel boxes in $\mathbb R^d$, with $|A|=n$ and $|B|=m$, where $m=\operatorname{poly}(n)$. Let $G_{A,B}$ be their intersection graph, and defin…

Let $[0,1]^d$ be the $d$-dimensional unit cube, and let … where … Write $d_{\mathcal{B}_{\rm per}}$ for the VC-dimension of this set system. Linear VC-dimension conjecture. The VC-…