Spanning trees whose stems have at most k leaves

Let T be a tree. A vertex of T with degree one is called a leaf, and the set of leaves of T is denoted by Leaf(T ). The subtree T − Leaf(T ) of T is called the stem of T and denoted by Stem(T ). A spanning tree with specified stem was first considered in [3]. A tree whose maximum degree at most k is called a k-tree. Similarly, a stem whose maximum degree at most k in it is called a k-stem, and a tree whose stem is k-tree is called a tree with k-stem. For an integer k ≥ 2 and a graph G, σk(G) denotes the minimum degree sum of k independent vertices of G. The following theorem gives a sufficient condition using σk(G) for a graph to have a spanning tree with k-stem.