Coloring intersection graph of squares

It is known that the coloring intersection graph of axis-parallel rectangles is NP-Hard. What about squares and more specific case "unit squares"?

Thanks.

Since coloring is a "harder" problem, it should also be NP-hard. A constant approximation follows as if a point is covered by $$k$$ squares, then the chromatic number is at least $$k$$, and it is not hard to color such a graph using $$O(k)$$ colors, observing that the intersection graph has $$O(nk)$$ edges.