  The renormalization group technique is applied to one-dimensional
electron-phonon Hubbard models at half-filling and zero temperature. For the
Holstein-Hubbard model, the results of one-loop calculations are congruent with
the phase diagram obtained by quantum Monte Carlo simulations in the $(U,g_{\rm
ph})$ plane for the phonon-mediated interaction $g_{\rm ph}$ and the Coulomb
interaction $U$. The incursion of an intermediate phase between a fully gapped
charge-density-wave state and a Mott antiferromagnet is supported along with
the growth of its size with the molecular phonon frequency $\omega_0$. We find
additional phases enfolding the base boundary of the intermediate phase. A
Luttinger liquid line is found below some critical $ U^*\approx g^*_{\rm ph}$,
followed at larger $U\sim g_{\rm ph}$ by a narrow region of bond-order-wave
ordering which is either charge or spin gapped depending on $U$. For the
Peierls-Hubbard model, the region of the $(U,g_{\rm ph})$ plane with a fully
gapped Peierls-bond-order-wave state shows a growing domination over the Mott
gapped antiferromagnet as the Debye frequency $\omega_D$ decreases. A power law
dependence $g_{\rm ph} \sim U^{2\eta}$ is found to map out the boundary between
the two phases, whose exponent is in good agreement with the existing quantum
Monte Carlo simulations performed when a finite nearest-neighbor repulsion term
$V$ is added to the Hubbard interaction.
