Gorenstein polytopes obtained from bipartite graphs

Details Gorenstein polytopes obtained from bipartite graphs Gorenstein polytopes obtained from bipartite graphs

2008-03-07

arxiv.org/abs/0803.1033v2

Mathematics

Combinatorics

11 pages, 5 figures

Scientific paper

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.

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