On the Gorenstein property of the Ehrhart ring of the stable set polytope of an h-perfect graph

Abstract

In this paper, we give a criterion of the Gorenstein property of the Ehrhart ring of the stable set polytope of an h-perfect graph: the Ehrhart ring of the stable set polytope of an h-perfect graph $G$ is Gorenstein if and only if (1) sizes of maximal cliques are constant (say $n$) and (2) (a) $n=1$, (b) $n=2$ and there is no odd cycle without chord and length at least 7 or (c) $n\ge 3$ and there is no odd cycle without chord and length at least 5.

Added an example, which shows that the symbolic powers of the canonical ideal of the Ehrhart ring of HSTAB(G) of a graph G is not equal to the ordinary power in general

References in corpus (1)

• Special simplices and Gorenstein toric rings