A 5k kernel for P2-packing in net-free graphs - Maw-Shang Chang; Li-Hsuan Chen; Ling-Ju Hung (ICSEC : 2014 International Computer Science and Engineering Conference : July 30, 2014-August 1, 2014, 2014)
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.