Spanning trees with a bounded number of leaves

n 1998, H. Broersma and H. Tuinstra proved that: Given a connected graph G with n ≥ 3 vertices, if d(u) + d(y) ≥n — k + 1 for all non-adjacent vertices u and v of G (k ≥ 1), then G has a spanning tree with at most k leaves. In this paper, we generalize this result by using implicit degree sum condition of t (2≤ t ≤k) independent vertices and we prove what follows: Let G be a connected graph on n ≥ 3 vertices and k ≥ 2 be an integer. If the implicit degree sum of any t independent vertices is at least [formula] for (k≥ t ≥ 2), then G has a spanning tree with at most k leaves.