  We investigated the phase diagram of $SU(3)$ gauge theory in four dimension
with one compact dimension by using the perturbative one-loop effective
potential. Effects of the adjoint and fundamental fermions are investigated and
then the rich phase structure in the quark-mass and compact-size scale is
realized. Our results are qualitatively consistent with the recent lattice
calculation and clearly show that the lattice calculation can be understood
from the Hosotani mechanism. Moreover, we show the result obtained by using the
flavor twisted boundary condition for fundamental fermion which does not break
the $Z_3$ symmetry, explicitly.
