Let F be a fixed edge-colored graph. The authors consider the problem of packing the greatest possible number of vertex disjoint copies of F into a given complete edge-colored graph. They observe that this problem is NP-hard unless F consists of isolated vertices and edges or unless there are only two colors and F is properly 2-edge-colored. Of the remaining problems the authors focus on the case where F is a properly 2-edge-colored path of length 2, when they show polynomial solutions based on matching methods. In fact, the authors prove that a large packing exists if and only if each color class has a matching of a sufficiently large size. They also consider the more general problem where ℱ is a fixed family of edge-colored graphs, and an edge-colored complete graph is to be packed with vertex disjoint copies of members of ℱ. Here the authors concentrate on two cases in which ℱ consist of trees and give sufficient conditions that guarantee the existence of a packing of given size.
