Bounds on the regularity and projective dimension of ideals associated to graphs

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...

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Bibliographic Details
Published inJournal of algebraic combinatorics Vol. 38; no. 1; pp. 37 - 55
Main Authors Dao, Hailong, Huneke, Craig, Schweig, Jay
Format Journal Article
LanguageEnglish
Published Boston Springer US 01.08.2013
Subjects
Combinatorics
Computer Science
Convex and Discrete Geometry
Group Theory and Generalizations
Lattices
Mathematics
Mathematics and Statistics
Order
Ordered Algebraic Structures
Edge ideals
Serre’s condition
Regularity
Projective dimension
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ISSN0925-9899
1572-9192
1572-9192
DOI10.1007/s10801-012-0391-z

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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.
ISSN:0925-9899
1572-9192
1572-9192
DOI:10.1007/s10801-012-0391-z