  In this article, we discuss the vertex decomposability of three well-studied
simplicial complexes associated to forests. In particular, we show that the
bounded degree complex of a forest and the complex of directed trees of a
multidiforest are vertex decomposable. We then prove that the non-cover complex
of a forest is either contractible or homotopy equivalent to a sphere. Finally,
we provide a complete characterization of forests whose non-cover complexes are
vertex decomposable.
