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In this paper we study two types of edge-disjoint packings of graphs. The induced edgedisjoint 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 share an edge. We 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 asksdoi:10.1016/0166-218x(92)00153-d fatcat:xjlp5zevqfb5dkq4d62it7f6ja