Complete-factors and f-factors

Abstract 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.