2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/68218In this paper we study simplicial complexes as higher dimensional graphs in order to produce algebraic statements about their facet ideals. We introduce a large class of square-free monomial ideals with Cohen-Macaulay quotients, and a criterion for the Cohen-Macaulayness of facet ideals of simplicial trees. Along the way, we generalize several concepts from graph theory to simplicial complexes.28 pages, 17 figuresCommutative AlgebraCombinatorics13, 05text