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For a finite collection of graphs ${\cal F}$, the \textsc{${\calF}$-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 ${\cal F}$ as atopological minor. We prove that for every such ${\cal F}$, \textsc{${\calF}$-TM-Deletion} is fixed parameter tractable on planar graphs. Our algorithmruns 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 tographs that are embeddable on any fixed surface.

Hitting Topological Minor Models in Planar Graphs is Fixed Parameter Tractable