Star-factors with large components

For a set H of connected graphs, a spanning subgraph H of a graph G is an H -factor if every component of H is isomorphic to some member of H . Amahashi and Kano [A. Amahashi, M. Kano, On factors with given components, Discrete Math. 42 (1982) 1–6] proved that a graph G satisfying i ( G − S ) ≤ m | S | for every S ⊂ V ( G ) has a { K 1 , l : 1 ≤ l ≤ m } -factor, where i ( G ) is the number of isolated vertices in G and K 1 , l denotes the star with l edges. Here we exclude small stars from the set and prove that a graph G satisfying i ( G − S ) ≤ 1 m | S | for every S ⊂ V ( G ) has a { K 1 , l : m ≤ l ≤ 2 m } -factor.