Geodesic
Regularity of powers of forests and cycles
Journal of Algebraic Combinatorics, Tome 42 (2015) no. 4, pp. 1077-1095.

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

Let $G$ be a graph and let $I = I(G)$ be its edge ideal. In this paper, when $G$ is a forest or a cycle, we explicitly compute the regularity of $I^s$ for all $s \ge 1$. In particular, for these classes of graphs, we provide the asymptotic linear function ${\mathrm{reg}}(I^s)$ as $s \gg 0$, and the initial value of $s$ starting from which ${\mathrm{reg}}(I^s)$ attains its linear form. We also give new bounds on the regularity of $I$ when $G$ contains a Hamiltonian path and when $G$ is a Hamiltonian graph.
Classification : 13D45, 05C38
Keywords: regularity, powers of ideal, edge ideal 
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     title = {Regularity of powers of forests and cycles},
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Beyarslan, Selvi; Hà, Huy Tài; Trung, Trân Nam. Regularity of powers of forests and cycles. Journal of Algebraic Combinatorics, Tome 42 (2015) no. 4, pp. 1077-1095. http://geodesic.mathdoc.fr/item/JAC_2015__42_4_a3/