University of Isfahan Transactions on Combinatorics 2251-8657 11 1 2022 03 01 Vertex decomposability of complexes associated to forests 1 13 25654 10.22108/toc.2021.127059.1809 EN Anurag Singh Department of Mathematics, Chennai Mathematical Institute, Kelambakkam, Chennai, India Journal Article 2021 01 17 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 https://toc.ui.ac.ir/article_25654_6acf776ce2921143525fd1fb0237d77b.pdf