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

2020/05/07 by Mitsuhiro Miyazaki, Miyazaki, Mitsuhiro · 2 citations
Mathematics · #Commutative Algebra and Its Applications #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models

paper · pdf · doi:10.48550/arxiv.2005.03259

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≥ 3 and there is no odd cycle without chord and length at least 5.

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