  }We study (vertex-disjoint) $P_2$-packings in graphs under a parameterized
perspective. Starting from a maximal $P_2$-packing $\p$ of size $j$ we use
extremal arguments for determining how many vertices of $\p$ appear in some
$P_2$-packing of size $(j+1)$. We basically can 'reuse' $2.5j$ vertices. We
also present a kernelization algorithm that gives a kernel of size bounded by
$7k$. With these two results we build an algorithm which constructs a
$P_2$-packing of size $k$ in time $\Oh^*(2.482^{3k})$.
