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) $n\geq 3$ and there is no odd cycle without chord and length at least 5.

Keywords

• Gorenstein ring
• h-perfect graph
• Ehrhart ring
• stable set polytope

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