Complete-factors and f-factors

A factor F of a graph is called a complete-factor if each component of F is complete. Let G be a graph, F be a complete-factor of G with ω(F)⩾2, and f be an integer-valued function defined on V(G) with ∑x∈V(G)f(x) even. If G−V(C) has an f-factor for each component C of F, then G has an f-factor.