Covering a subset with two cycles

Let G be a graph of order n. Let W be a subset of V (G) with |W | ≥ 6. We show that if d(x) ≥ 2n/3 for each x ∈ W , then for any partition |W | = n1 + n2 with n1 ≥ 3 and n2 ≥ 3, G contains two vertex-disjoint cycles C1 and C2 such that C1 contains n1 vertices of W and C2 contains n2 vertices of W .