  In the DELETION TO INDUCED MATCHING problem, we are given a graph $G$ on $n$
vertices, $m$ edges and a non-negative integer $k$ and asks whether there
exists a set of vertices $S \subseteq V(G) $ such that $|S|\le k$ and the size
of any connected component in $G-S$ is exactly 2. In this paper, we provide a
fixed-parameter tractable (FPT) algorithm of running time $O^*(1.748^{k})$ for
the DELETION TO INDUCED MATCHING problem using branch-and-reduce strategy and
path decomposition. We also extend our work to the exact-exponential version of
the problem.
