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Given an input graph G and an integer k, the parameterized K_4-minor coverproblem asks whether there is a set S of at most k vertices whose deletionresults in a K_4-minor-free graph, or equivalently in a graph of treewidth atmost 2. This problem is inspired by two well-studied parameterized vertexdeletion problems, Vertex Cover and Feedback Vertex Set, which can also beexpressed as Treewidth-t Vertex Deletion problems: t=0 for Vertex Cover and t=1for Feedback Vertex Set. While a single-exponential FPT algorithm has beenknown for a long time for \textsc{Vertex Cover}, such an algorithm for FeedbackVertex Set was devised comparatively recently. While it is known to be unlikelythat Treewidth-t Vertex Deletion can be solved in time c^{o(k)}.n^{O(1)}, itwas open whether the K_4-minor cover problem could be solved insingle-exponential FPT time, i.e. in c^k.n^{O(1)} time. This paper answers thisquestion in the affirmative.

A single-exponential FPT algorithm for the $K_4$-minor cover problem