Gorenstein homogeneous subrings of graphs

@article{Cruz2022GorensteinHS,
  title={Gorenstein homogeneous subrings of graphs},
  author={Lourdes Cruz and Enrique Reyes and Jonathan Toledo},
  journal={Journal of Algebra and Its Applications},
  year={2022}
}
Let G = (V, E) be a connected simple graph, with n vertices such that S is its homogeneous monomial subring. We prove that if S is normal and Gorenstein, then G is unmixed with cover number ⌈n 2 ⌉ and G has a strong ⌈n 2 ⌉-τ -reduction. Furthermore, if n is even, then we show that G is bipartite. Finally, if S is normal and G is unmixed whose cover number is ⌈n 2 ⌉, we give sufficient conditions for S to be Gorenstein. 

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