  We construct the equation of state (EoS) for neutron stars explicitly
including hyperons and quarks. Using the quark-meson coupling model with
relativistic Hartree-Fock approximation, the EoS for hadronic matter is derived
by taking into account the strange ($\sigma^{\ast}$ and $\phi$) mesons as well
as the light non-strange ($\sigma$, $\omega$, $\vec{\pi}$ and $\vec{\rho}$)
mesons. Relevant coupling constants are determined to reproduce the
experimental data of nuclear matter and hypernuclei in SU(3) flavor symmetry.
For quark matter, we employ the MIT bag model with one-gluon-exchange
interaction, and Gibbs criteria for chemical equilibrium in the phase
transition from hadrons to quarks. We find that the strange vector ($\phi$)
meson and the Fock contribution make the hadronic EoS stiff, and that the
maximum mass of a neutron star can be consistent with the observed mass of
heavy neutron stars even if the coexistence of hadrons and quarks takes place
in the core. However, in the present calculation the transition to pure quark
matter does not occur in stable neutron stars. Furthermore, the lower bound of
the critical chemical potential of the quark-hadron transition at zero
temperature turns out to be around 1.5 GeV in order to be consistent with the
recent observed neutron star data.
