2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/65163This paper starts with an observation that two infinite series of simplicial complexes, which a priori do not seem to have anything to do with each other, have the same homotopy type. One series consists of the complexes of directed forests on a double directed string, while the other one consists of Shapiro-Welker models for the spaces of hyperbolic polynomials with a triple root. We explain this coincidence in the more general context by finding an explicit homotopy equivalence between complexes of directed forests on a double directed tree, and doubly disconnecting complexes of a tree.General TopologyAlgebraic TopologyCombinatorics57Q05; 05C05, 58K15text