In this paper the authors study two types of edge-disjoint packings of graphs. The induced edge-disjoint G packing problem is: given graph H and integer k, does H contain at least k copies of G as induced subgraphs such that no two such copies of G shares an edge. The authors show that if G has at most two edges then the induced edge-disjoint G packing problem belongs to P, whereas for all other graphs G the problem is NP-complete. The second edge-disjoint packing problem concerns partial subgraphs and asks whether a given graph H contains at least k copies G as partial subgraphs such that no two such copies of G share an edge. The authors show that if G has any connected component with at least three edges then this problem is NP-complete.
