Let T be a tree. Then a vertex of T with degree one is a leaf of T and a vertex of degree at least three is a branch vertex of T. The set of leaves of T is denoted by L(T) and the set of branch vertices of T is denoted by B(T). For two distinct vertices u, v of T, let P_T[u, v] denote the unique path in T connecting u and v. Let T be a tree with B(T) ≠ ∅. For each leaf x of T, let y_x denote the nearest branch vertex to x. We delete V(P_T[x, y_x]) {y_x} from T for all x ∈ L(T). The resulting subtree of T is called the reducible stem of T and denoted by R_Stem(T). We give sharp sufficient conditions on the degree sum for a graph to have a spanning tree whose reducible stem has a few branch vertices.

设T为一棵树。然后的顶点Ť与度之一是一个叶Ť和至少三个度的顶点的一个分支顶点Ť。该组叶Ť由表示大号（Ť）和设定的分支顶点Ť由表示乙（Ť）。对于两个不同的顶点U，V的Ť，让P _Ť [ U，V ]表示在唯一路径Ť连接Ú和v。设T是一棵B的树( T ) ≠ ∅。对于每个叶X的Ť，让ÿ _X表示最近的分支的顶点到X。对于所有x ∈ L ( T )，我们从T 中删除V ( P _T [ x, y _x ]) { y _x } 。将所得的子树Ť被称为的还原干Ť和由R_Stem（表示Ť）。我们给出了一个图的度和的尖锐充分条件，它有一个生成树，它的可约树干有几个分支顶点。