For a planar graph $H$, let $f(H)$ denote the minimum integer such that all graphs excluding $H$ as a minor have treewidth at most $f(H)$. We show that if $H$ is a disjoint union of $k$ cycles then $f(H)=O(|V(H)| + k \log k)$, which is best possible.

翻译：对于平面图$H$，令$f(H)$表示最小整数，使得所有将$H$排除作为子式的图的树宽度至多为$f(H)$。我们证明，若$H$是$k$个循环的不相交并，则$f(H)=O(|V(H)| + k \log k)$，该结果是最优的。