  In the $l$-path vertex cover problem the input is an undirected graph $G$ and
an integer $k$. The goal is to decide whether there is a set of vertices $S$ of
size at most $k$ such that $G-S$ does not contain a path with $l$ vertices. In
this paper we give parameterized algorithms for $l$-path vertex cover for $l =
5,6,7$, whose time complexities are $O^*(3.945^k)$, $O^*(4.947^k)$, and
$O^*(5.951^k)$, respectively.
