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.
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