Gorenstein homogeneous subrings of graphs

  title={Gorenstein homogeneous subrings of graphs},
  author={Lourdes Cruz and Enrique Reyes and Jonathan Toledo},
  journal={Journal of Algebra and Its Applications},
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. 

Figures from this paper


Very well covered graphs
Well-covered graphs and factors
Systems with the integer rounding property in normal monomial subrings
Let C be a clutter and let A be its incidence matrix. If the linear system x ≥ 0; x A ≤ 1 has the integer rounding property, we give a description of the canonical module and the a-invariant of
Duality, a-invariants and canonical modules of rings arising from linear optimization problems
The aim of this paper is to study integer rounding properties of various systems of linear inequalities to gain insight about the algebraic properties of Rees algebras of monomial ideals and monomial
ContentsIntroductionChapter I. Affine toric varieties § 1. Cones, lattices, and semigroups § 2. The definition of an affine toric variety § 3. Properties of toric varieties § 4. Differential forms on
Monomial Algebras (Second Edition, Monographs and Research
  • Notes in Mathematics, Chapman and Hall/CRC,
  • 2015
Unmixed bipartite graphs
espanolEn esta nota nosotros presentamos una caracterizacion combinatoria de todos los grafos bipartitos no-mezcladas. \keywords{Grafos no-mezclados, cubrimiento de vertices minimo, grafos
Cohen-Macaulay Rings (Cambridge
  • 1997
Unmixed bipartite graphs, Rev
  • Colombiana Mat
  • 2007