  Given a graph $G$ and sets $\{\alpha_v~|~v \in V(G)\}$ and $\{\beta_v~|~v \in
V(G)\}$ of non-negative integers, it is known that the decision problem whether
$G$ contains a spanning tree $T$ such that $\alpha_v \le d_T (v) \le \beta_v $
for all $v \in V(G)$ is $NP$-complete. In this article, we relax the problem by
demanding that the degree restrictions apply to vertices $v\in U$ only, where
$U$ is a stable set of $G$. In this case, the problem becomes tractable.
  A. Frank presented a result characterizing the positive instances of that
relaxed problem. Using matroid intersection developed by J. Edmonds, we give a
new and short proof of Frank's result and show that if $U$ is stable and the
edges of $G$ are weighted by arbitrary real numbers, then even a minimum-cost
tree $T$ with $\alpha_v \le d_T (v) \le \beta_v $ for all $v \in U$ can be
found in polynomial time if such a tree exists.
