Edge ideals whose all matching powers are bi-Cohen-Macaulay

Abstract

We classify all graphs $G$ satisfying the property that all matching powers $I(G{)}^{[k]}$ of the edge ideal $I(G)$ are bi-Cohen-Macaulay for $1\le k\le \hat{I}½(G)$, where $\hat{I}½(G)$ is the maximum size of a matching of $G$.

Final version of the paper accepted for publication in Communications in Algebra