Abstract:

Suppose $I$ is a squarefree monomial ideal whose generators all have degree 2. Then we may think of $I$ as the edge ideal of a simple graph $G$. Ralf Fröberg showed that the minimal resolution of such an ideal is linear precisely when the complementary graph, $G^c$, is chordal. In his proof Fröberg uses the fact that there are several equivalent descriptions of chordal graphs.

In this talk I will describe a class of hypergraphs that generalizes the class of chordal graphs. We will use $d$-flag complexes, a generalization of flag complexes.