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 fast growing function $f(t)$. Moreover, our proof is short and simple.

翻译：设$T$为具有$t$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$k$个两两顶点不相交且各自具有$T$小元的子图，要么存在一个至多包含$t(k-1)$个顶点的集合$X$，使得$G-X$不包含$T$小元。该关于$X$大小的界是最优的，并且改进了Fiorini、Joret和Wood（2013年）证明的早期$f(t)k$界（其中$f(t)$为某个快速增长函数）。此外，我们的证明简短而简洁。