Rainbow H-factors

An H-factor of a graph G is a spanning subgraph of G whose connected components are isomorphic to H. Given a properly edge-colored graph G, a rainbow H-subgraph of G is an H-subgraph of G whose edges have distinct colors. A rainbow H-factor is an H-factor whose components are rainbow H-subgraphs. The following result is proved. If H is any fixed graph with h vertices then every properly edge-colored graph with hn vertices and minimum degree (1 − 1/χ(H))hn + o(n) has a rainbow H-factor.