# Feedback Vertex Set restricted to planar graphs

In Feedback Vertex Set, we are given an undirected graph $$G$$ and $$k \in \mathbb{N}$$, and the objective is to decide whether there exists a subset $$S \subseteq V(G)$$ of size at most $$k$$ such that $$G-S$$ is a forest. How can I solve it in running time complexity of $$k^{O(\sqrt{k})} n^{O(1)}$$ when restricted to planar graphs?

• What are your thoughts? Where does this come up? Jul 6 '21 at 10:51