# Hitting minors on bounded treewidth graphs. II. Single-exponential algorithms

For a finite collection of graphs F, the F-M-DELETION (resp. F-TM-DELETION) problem consists in, given a graph G and an integer k, decide whether there exists S ⊆ V(G) with |S| ≤ k such that G ∖ S does not contain any of the graphs in F as a minor (resp. topological minor). We are interested in the parameterized complexity of both problems when the parameter is the treewidth of G, denoted by tw, and specifically in the cases where F contains a single connected planar graph H. We present algorithms running in time 2^O(tw)· n^O(1), called single-exponential, when H is either P_3, P_4, C_4, the paw, the chair, and the banner for both {H}-M-DELETION and {H}-TM-DELETION, and when H=K_1,i, with i ≥ 1, for {H}-TM-DELETION. Some of these algorithms use the rank-based approach introduced by Bodlaender et al. [Inform Comput, 2015]. This is the second of a series of articles on this topic, and the results given here together with other ones allow us, in particular, to provide a tight dichotomy on the complexity of {H}-M-DELETION in terms of H.

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