Geodesic
A lower bound for depths of powers of edge ideals
Journal of Algebraic Combinatorics, Tome 42 (2015) no. 3, pp. 829-848.

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

Let $G$ be a graph, and let $I$ be the edge ideal of $G$. Our main results in this article provide lower bounds for the depth of the first three powers of $I$ in terms of the diameter of $G$. More precisely, we show that depth $R/I^t\geq\left\lceil\frac{d-4t+5}{3}\right\rceil+p-1$, where $d$ is the diameter of $G$ and $p$ is the number of connected components of $G$ and $1\leq t\leq 3$. For general powers of edge ideals we show that depth $R/I^t\geq p-t$. As an application of our results we obtain the corresponding lower bounds for the Stanley depth of the first three powers of $I$.
Classification : 05E40
Keywords: depth, Stanley depth, edge ideals 
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     title = {A lower bound for depths of powers of edge ideals},
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     url = {http://geodesic.mathdoc.fr/item/JAC_2015__42_3_a3/}
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Fouli, Louiza; Morey, Susan. A lower bound for depths of powers of edge ideals. Journal of Algebraic Combinatorics, Tome 42 (2015) no. 3, pp. 829-848. http://geodesic.mathdoc.fr/item/JAC_2015__42_3_a3/