  We show that provided $\log^{50} n/n \leq p \leq 1 - n^{-1/4}\log^9 n$ we can
with high probability find a collection of $\lfloor \delta(G)/2 \rfloor$
edge-disjoint Hamilton cycles in $G \sim G_{n, p}$, plus an additional
edge-disjoint matching of size $\lfloor n/2 \rfloor$ if $\delta(G)$ is odd.
This confirms, for the above range of $p$, a conjecture of Frieze and
Krivelevich.
