  In this paper, we consider the averaging principle for a class of
McKean-Vlasov stochastic differential equations with slow and fast time-scales.
Under some proper assumptions on the coefficients, we first prove that the slow
component strongly converges to the solution of the corresponding averaged
equation with convergence order $1/3$ using the approach of time
discretization. Furthermore, under stronger regularity conditions on the
coefficients, we use the technique of Poisson equation to improve the order to
$1/2$, which is the optimal order of strong convergence in general.

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