2 problems

Non-expanding links conjecture. There is no sequence of bounded-degree finite graphs, with size growing to infinity, such that all links in all the graphs form an expander family.

Let $A\subset\mathbb{R}$ be a finite set, and for a positive integer $k$ write … Here $X\gg_{k,l}Y$ means that $X\geq c_{k,l}Y$ for a positive constant depending only on $k$ and…