Geodesic
Bounds on the regularity and projective dimension of ideals associated to graphs
Journal of Algebraic Combinatorics, Tome 38 (2013) no. 1, pp. 37-55.

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

Summary: In this paper, we give new upper bounds on the regularity of edge ideals whose resolutions are k-step linear; surprisingly, the bounds are logarithmic in the number of variables. We also give various bounds for the projective dimension of such ideals, generalizing other recent results. By Alexander duality, our results also apply to unmixed square-free monomial ideals of codimension two. We also discuss and connect these results to more classical topics in commutative algebra.
Keywords: projective dimension, regularity, edge ideals, Serre's condition 
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     title = {Bounds on the regularity and projective dimension of ideals associated to graphs},
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Dao, Hailong; Huneke, Craig; Schweig, Jay. Bounds on the regularity and projective dimension of ideals associated to graphs. Journal of Algebraic Combinatorics, Tome 38 (2013) no. 1, pp. 37-55. http://geodesic.mathdoc.fr/item/JAC_2013__38_1_a9/