A Problem kernelization for graph packing

Abstract

For a fixed connected graph H, we consider the NP-complete H-packing problem, where, given an undirected graph G and an integer k = 0, one has to decide whether there exist k vertex-disjoint copies of H in G. We give a problem kernel of O(k|V (H)|-1) vertices, that is,we provide a polynomial-time algorithm that reduces a given instance of H-packing to an equivalent instance with at most O(k|V (H)|-1) vertices. In particular, this result specialized to H being a triangle improves a problem kernel for Triangle Packing from O(k3) vertices by Fellows et al. [WG 2004] to O(k2) vertices. © Springer-Verlag Berlin Heidelberg 2009.