Shellability of Complexes of Trees

Abstract

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. © 1998 Academic Press.