Intersection graphs of squares and rectangles Is it known if the class of intersection graphs of rectangles is equal to the class of intersection graphs of squares (not necessarily unit)?
See "Squarability of rectangle arrangements", Konečný, Kučera, Opler, Sosnovec, Šimsa, and Töpfer, CCCG 2016. In particular their Theorem 6 proves for all $d$ the existence of graphs with boxicity 2 and cubicity $d$.