For a finite collection of graphs $\mathcal{F}$, the $\mathcal{F}$-TM-Deletion problem has as input an $n$-vertex graph $G$ and an integer $k$ and asks whether there exists a set $S \subseteq V(G)$ with $|S| \leq k$ such that $G \setminus S$ does not contain any of the graphs in $\mathcal{F}$ as a topological minor. We prove that for every such $\mathcal{F}$, $\mathcal{F}$-TM-Deletion is fixed parameter tractable on planar graphs. Our algorithm runs in a $2^{\mathcal{O}(k^2)}\cdot n^{2}$ time or, alternatively in $2^{\mathcal{O}(k)}\cdot n^{4}$ time. Our techniques can easily be extended to graphs that are embeddable to any fixed surface.

翻译：对于数量有限的图表收藏 $\ mathcal{ F} $\ mathcal{ F} $- TM- delettion 问题,$\ mathcal{ F} $- TM- delettion 问题作为输入输入了 $n- verex 图形 $G$ 和 整数 $k$, 询问是否有一套 $S\ subseqeq V( G) $ @ @\\\\\\\\\ leq k$, 这样, $G\ setminus S$ 并不包含任何以 $\ mathcal{ F} 表示的图表 。 我们的技术可以很容易地扩展为可嵌入任何固定表面的图形 。