  We propose a hole decomposition scheme to exactly solve a class of spin-1
quantum Ising models with transverse or longitudinal single-ion anisotropy. In
this scheme, the spin-1 model is mapped onto a family of the $S=1/2$ transverse
Ising models, characterized by the total number of holes. A recursion formula
is derived for the partition function based on the reduced $S=1/2$ Ising model.
This simplifies greatly the summation over all the hole configurations. It
allows the thermodynamic quantities to be rigorously determined in the
thermodynamic limit. The ground state phase diagram is determined for both the
uniform and dimerized spin chains. The corresponding thermodynamic properties
are calculated and discussed.
