Coloring the complements of intersection graphs of geometric figures

Let be the complement of the intersection graph G of a family of translations of a compact convex figure in Rⁿ. When n=2, we show that , where γ(G) is the size of the minimum dominating set of G. The bound on is sharp. For higher dimension we show that , for n?3. We also study the chromatic number of the complement of the intersection graph of homothetic copies of a fixed convex body in Rⁿ.