Shellability of Complexes of Trees

We show that for allk⩾1 andn⩾0 the simplicial complexes T(k)nof all leaf-labelled trees withnk+2 leaves and all interior vertices of degreeskl+2 (l⩾1) are shellable. This yields a direct combinatorial proof that they are Cohen–Macaulay and that their homotopy types are wedges of spheres.