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 give a quadratic kernel for packing k copies of H=K₁,s. 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 O(2⁵‧³⁰¹ᵏk²‧⁵+n³)