Looking at the Stars

The problem of packing k vertex-disjoint copies of a graph H into another graph G is NP-complete if H has more than two vertices in some connected component. In the framework of parameterized complexity we analyze a particular family of instances of this problem, namely the packing of stars. We prove that packing k copies of H = K_{1, s} is fixed-parameter tractable and give a quadratic kernel for the general case. When we consider the special case of s=2, i.e. H being a star with two leaves, we give a linear kernel and an algorithm running in time ${\mathcal O}^*(2^{5.3k})$.