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 : 13 | Download : 9

Publication Date : 2021-07-17

Article Type : Research Paper

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 insert ignore into journalissuearticles values(1); sizes of maximal cliques are constant insert ignore into journalissuearticles values(say $n$); and insert ignore into journalissuearticles values(2); insert ignore into journalissuearticles values(a); $n=1$, insert ignore into journalissuearticles values(b); $n=2$ and there is no odd cycle without chord and length at least 7 or insert ignore into journalissuearticles values(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