Before revision:  This problem was first studied in \mbox{%DIFAUXCMD lubars2018correcting0pt%DIFAUXCMD where an algorithm is proposed and shown to perfectly recover the correct vertex mapping with high probability if \beta\geq\max} \frac{8{3}p,
After revision:  0pt%DIFAUXCMD where an algorithm is proposed and shown to perfectly recover the correct vertex mapping with high probability if \beta\geq\max} \frac{8{3}p,