3 problems

Let $d\geq 2$ be an integer, and consider the class of graphs with sphere dimension at most $d$. Quasi-isometry conjecture. This class is quasi-isometric to the class of intersecti…

Let $d\geq 1$ be an integer, and consider the class of graphs whose sphere dimension is at most $d$. Asymptotic-dimension conjecture. This class has asymptotic dimension at most…

Let $t,d greater than or equal to 1$ be integers, and let $G$ be an $n$-vertex graph in the class $SphereInt{d}t$ of sphere intersection graphs. A balanced separator is a vertex se…