Anurag Singh - Department of Mathematics, Chennai Mathematical Institute, Kelambakkam, Chennai, India

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 is 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.

‎Bounded degree complex‎, ‎non-cover complex‎, ‎complex of directed trees‎, ‎vertex decomposable complex‎, ‎forests