  Recently precise results for the boundary between the Mott insulator phase
and the superfluid phase of the homogeneous Bose-Hubbard model have become
available for arbitrary integer filling factor g and any lattice dimension d >
1. We use these data for demonstrating that the critical hopping parameters
obey a scaling relationship which allows one to map results for different g
onto each other. Unexpectedly, the mean-field result captures the dependence of
the exact critical parameters on the filling factor almost fully. We also
present an approximation formula which describes the critical parameters for d
> 1 and any g with high accuracy.
