Hitting Topological Minor Models in Planar Graphs is Fixed Parameter Tractable

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