Cohen-Macaulay, Shellable and unmixed clutters with a perfect matching of König type

Susan Morey, Enrique Reyes, Rafael H. Villarreal

Let $\mathcal{C}$ be a clutter with a perfect matching $e_1,...,e_g$ of König type and let ${\Delta }_{\mathcal{C}}$ be the Stanley-Reisner complex of the edge ideal of $\mathcal{C}$. If all…