ON THE GORENSTEIN PROPERTY OF THE EHRHART RING OF THE STABLE SET POLYTOPE OF AN H-PERFECT GRAPH

Year 2021, Volume: 30 Issue: 30, 269 - 284, 17.07.2021

Mitsuhiro Mıyazakı

https://doi.org/10.24330/ieja.969935

Cited By: 4

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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