On contact graphs of totally separable packings in low dimensions

We give upper bounds on the maximum degree (called separable Hadwiger number) and the maximum number of edges (called separable contact number) of the contact graph of a totally separable packing of n translates of an arbitrary smooth convex body in Ed with d=2,3,4. In the proofs, linear algebraic and convexity methods are combined with volumetric and packing density estimates based on the underlying isoperimetric (resp., reverse isoperimetric) inequality.