Let $T$ be a tree on $t$ vertices. We prove that for every positive integer $k$ and every graph $G$, either $G$ contains $k$ pairwise vertex-disjoint subgraphs each having a $T$ minor, or there exists a set $X$ of at most $t(k-1)$ vertices of $G$ such that $G-X$ has no $T$ minor. The bound on the size of $X$ is best possible and improves on an earlier $f(t)k$ bound proved by Fiorini, Joret, and Wood (2013) with some very fast growing function $f(t)$. Moreover, our proof is very short and simple.

翻译：设 $T$ 为一棵有 $t$ 个顶点的树。我们证明：对于任意正整数 $k$ 和任意图 $G$，要么 $G$ 包含 $k$ 个两两顶点不交的、每个均含有 $T$ 作为 minors 的子图，要么存在一个大小不超过 $t(k-1)$ 的顶点子集 $X \subseteq V(G)$，使得 $G-X$ 不含 $T$ 作为 minor。该 $X$ 的大小上界是最优的，且改进了 Fiorini、Joret 和 Wood (2013) 以某个增长极快的函数 $f(t)$ 所证明的 $f(t)k$ 上界。此外，我们的证明非常简短。