its optimal decision tree. Then we apply Theorem \ref{topothm} combined with the
brute-force construction of optimal decision trees from Lemma \ref{odtconst}. Together they guarantee
that we can assign the decision trees to the subgraphs in time:
-$$\O(\Vert\C\Vert + t^{t(2t+1)} \cdot (2^{2^{4t^2}} + t^2)) = \O(m).$$
+$$\O\Bigl(\Vert\C\Vert + t^{t(2t+1)} \cdot \bigl(2^{2^{4t^2}} + t^2\bigr)\Bigr) = \O(m).$$
Execution of the decision tree on each subgraph~$C_i$ then takes $\O(D(C_i))$ steps.
The contracted graph~$G_A$ has at most $n/t = \O(n / \log^{(3)}n)$ vertices and asymptotically