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We show that with high probability the random graph $G_{n, 1/2}$ has aninduced subgraph of linear size, all of whose degrees are congruent to $r\pmodq$ for any fixed $r$ and $q\geq 2$.  More generally, the same is true for any fixed distribution of degrees modulo$q$.  Finally, we show that with high probability we can partition the vertices of$G_{n, 1/2}$ into $q+1$ parts of nearly equal size, each of which induces asubgraph all of whose degrees are congruent to $r\pmod q$.  Our results resolve affirmatively a conjecture of Scott, who addressed thecase $q=2$.

On subgraphs with degrees of prescribed residues in the random graph