Gorenstein polytopes obtained from bipartite graphs

TL;DR

This paper characterizes torus graphs with Gorenstein perfect matching polytopes and introduces a new class of polytopes from graphs, extending methods to construct numerous Gorenstein polytopes.

Contribution

It completes the characterization of Gorenstein perfect matching polytopes for torus graphs and introduces a new class of graph-derived Gorenstein polytopes with an extended construction method.

Findings

Characterized Gorenstein perfect matching polytopes for torus graphs.

Developed a new class of graph-based Gorenstein polytopes.

Extended construction methods for Gorenstein polytopes.

Abstract

Beck et. al. characterized the grid graphs whose perfect matching polytopes are Gorenstein and they also showed that for some parameters, perfect matching polytopes of torus graphs are Gorenstein. In this paper, we complement their result, that is, we characterize the torus graphs whose perfect matching polytopes are Gorenstein. Beck et. al. also gave a method to construct an infinite family of Gorenstein polytopes. In this paper, we introduce a new class of polytopes obtained from graphs and we extend their method to construct many more Gorenstein polytopes.