Packing problems in edge-colored graphs

AbstractLet F be a fixed edge-colored graph. We consider the problem of packing the greatest possible number of vertex disjoint copies of F into a given complete edge-colored graph. We 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 we focus on the case where F is a properly 2-edge-colored path of length 2, when we show polynomial solutions based on matching methods. In fact, we prove that a large packing exists if and only if each color class has a matching of a sufficiently large size. We 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 we concentrate on two cases in which F consists of trees and give sufficient conditions that guarantee the existence of a packing of given size