An improved kernelization for P2-packing

The P2-packing problem is a generalized matching problem and is known to be NP-hard. A kernelization algorithm for the parameterized P2-packing problem is a polynomial time algorithm that on an instance (G,k) of the problem produces another instance (G′,k′) such that k′⩽k and that (G,k) is a yes-instance if and only if (G′,k′) is a yes-instance. The graph G′ in the reduced instance is called a kernel. We provide new structural analysis and develop a new kernelization algorithm for the problem that produces a kernel of at most 7k vertices. This improves the previous best kernelization algorithm that produces a kernel of 15k vertices. Based on the new kernel, we present a parameterized algorithm of running time O∗(k17.66) for the problem, improving the previous best upper bound O∗(k32).