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