  We have constructed a pressure$-$temperature ($P-T$) phase diagram of
$P$-induced superconductivity in EuFe$_2$As$_2$ single crystals, via
resistivity ($\rho$) measurements up to 3.2 GPa. As hydrostatic pressure is
applied, an antiferromagnetic (AF) transition attributed to the FeAs layers at
$T_\mathrm{0}$ shifts to lower temperatures, and the corresponding resistive
anomaly becomes undetectable for $P$ $\ge$ 2.5 GPa. This suggests that the
critical pressure $P_\mathrm{c}$ where $T_\mathrm{0}$ becomes zero is about 2.5
GPa. We have found that the AF order of the Eu$^{2+}$ moments survives up to
3.2 GPa without significant changes in the AF ordering temperature
$T_\mathrm{N}$. The superconducting (SC) ground state with a sharp transition
to zero resistivity at $T_\mathrm{c}$ $\sim$ 30 K, indicative of bulk
superconductivity, emerges in a pressure range from $P_\mathrm{c}$ $\sim$ 2.5
GPa to $\sim$ 3.0 GPa. At pressures close to but outside the SC phase, the
$\rho(T)$ curve shows a partial SC transition (i.e., zero resistivity is not
attained) followed by a reentrant-like hump at approximately $T_\mathrm{N}$
with decreasing temperature. When nonhydrostatic pressure with a uniaxial-like
strain component is applied using a solid pressure medium, the partial
superconductivity is continuously observed in a wide pressure range from 1.1
GPa to 3.2 GPa.
