Cohen-Macaulay properties of square-free monomial ideals (Q1770438)

This paper deals with the facet ideals of some special simplicial complexes (called ``grafted'' by the author) in order to prove that their quotient ring is Cohen-Macaulay. This result provides a wealth of square-free monomial ideals with Cohen-Macaulay quotients, and also implies that all unmixed trees are Cohen-Macaulay. Along the way it is proved that \textit{R. H. Villarreal}'s Cohen-Macaulay criterion for graph-trees [Manuscr. Math. 66, 277--293 (1990; Zbl 0737.13003)] extends to simplicial trees, a notion defined here.