Geodesic
Koszulness, Krull dimension, and other properties of graph-related algebras
Journal of Algebraic Combinatorics, Tome 34 (2011) no. 3, pp. 375-400.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: The algebra of basic covers of a graph $G$, denoted by [ `$( A)]( G)$ barA$(G)$, was introduced by Herzog as a suitable quotient of the vertex cover algebra. In this paper we compute the Krull dimension of [ `$( A)]( G)$ barA$(G)$ in terms of the combinatorics of $G$. As a consequence, we get new upper bounds on the arithmetical rank of monomial ideals of pure codimension 2. Furthermore, we show that if the graph is bipartite, then [ `$( A)]( G)$ barA$(G)$ is a homogeneous algebra with straightening laws, and thus it is Koszul. Finally, we characterize the Cohen-Macaulay property and the Castelnuovo-Mumford regularity of the edge ideal of a certain class of graphs.
Keywords: keywords vertex covers of graphs, cover ideal, edge ideal, fiber cone, Koszul, straightening laws, Krull dimension, arithmetical rank, Cohen-Macaulay, Castelnuovo-Mumford regularity 
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     author = {Constantinescu, Alexandru and Varbaro, Matteo},
     title = {Koszulness, {Krull} dimension, and other properties of graph-related algebras},
     journal = {Journal of Algebraic Combinatorics},
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     url = {http://geodesic.mathdoc.fr/item/JAC_2011__34_3_a5/}
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Constantinescu, Alexandru; Varbaro, Matteo. Koszulness, Krull dimension, and other properties of graph-related algebras. Journal of Algebraic Combinatorics, Tome 34 (2011) no. 3, pp. 375-400. http://geodesic.mathdoc.fr/item/JAC_2011__34_3_a5/