= Solution
In the standard regularity-partition convention, the vertex sets form a disjoint partition, the nonexceptional sets $V_1,\ldots,V_k$ are nonempty and have a common size, $|V_0|<\epsilon|V(G)|$, and at most $\epsilon k^2$ unordered nonexceptional pairs fail to be $\epsilon$-uniform. One can instead use weak inequality for the exceptional-set bound without affecting the argument below once the size bound is strict. The exceptional set absorbs the rounding remainder when the <graph> order is not divisible by $k$.
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