A 5k kernel for P2-packing in net-free graphs

Given a graph G = (V, E), a P
₂
-packing P is a collection of vertex disjoint copies of P
₂
s in G where a P
₂
is a simple path with three vertices and two edges. The kP
₂
-Packing problem asks whether there exists a P
₂
-packing of size k in G by taking graph G and a fixed parameter k as the input. This problem is NP-hard for net-free graphs. In this paper, we give a kernelization algorithm for the kP
₂
-Packing problem in net-free graphs. We show that in polynomial time our kernelization algorithm obtains a size-5k kernel which is smaller than those kernels found by previous known kernelization algorithms.