  A $k$-tree is a spanning tree with every vertex of degree at most $k$. In
this paper, we provide some sufficient conditions, in terms of the (adjacency
and signless Laplacian) spectral radius, for the existence of a $k$-tree in a
connected graph of order $n$, and a perfect matching in a balanced bipartite
graph of order $2n$ with minimum degree $\delta$, respectively.
