  We prove basic theorems about the ground states of the S=1 Bose-Hubbard
model. The results are quite universal and depend only on the coefficient U_2
of the spin-dependent interaction. We show that the ground state exhibits
saturated ferromagnetism if U_2<0, is spin-singlet if U_2>0, and exhibits
"SU(3)-ferromagnetism" if U_2=0, and completely determine the degeneracy in
each region.
