An Improved Parameterized Algorithm for the Independent Feedback Vertex Set Problem

In this paper, we develop a new parameterized algorithm for the {\sc Independent Feedback Vertex Set} (IFVS) problem. Given a graph $G=(V,E)$, the goal of the problem is to determine whether there exists a vertex subset $F\subseteq V$ such that $V-F$ induces a forest in $G$ and $F$ is an independent set. We show that there exists a parameterized algorithm that can determine whether a graph contains an IFVS of size $k$ or not in time $O(4^kn^{2})$. To our best knowledge, this result improves the known upper bound for this problem, which is $O^{*}(5^{k}n^{O(1)})$.