- International Electronic Journal of Algebra
- Vol: 30 Issue: 30
- ON THE GORENSTEIN PROPERTY OF THE EHRHART RING OF THE STABLE SET POLYTOPE OF AN H-PERFECT GRAPH
ON THE GORENSTEIN PROPERTY OF THE EHRHART RING OF THE STABLE SET POLYTOPE OF AN H-PERFECT GRAPH
Authors : Mitsuhiro Miyazaki
Pages : 269-284
Doi:10.24330/ieja.969935
View : 10 | Download : 4
Publication Date : 2021-07-17
Article Type : Research
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