A lower bound for depths of powers of edge ideals

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 ≥ d - 4 t + 5 3 + p - 1 , where d is the diameter of G and p is the numbe...

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Bibliographic Details
Published inJournal of algebraic combinatorics Vol. 42; no. 3; pp. 829 - 848
Main Authors Fouli, Louiza, Morey, Susan
Format Journal Article
LanguageEnglish
Published New York Springer US 01.11.2015
Subjects
Combinatorics
Computer Science
Convex and Discrete Geometry
Group Theory and Generalizations
Lattices
Mathematics
Mathematics and Statistics
Order
Ordered Algebraic Structures
Monomial ideal
05E40
Edge ideal
Powers of ideals
Stanley depth
Projective dimension
Depth
13F55
13C15
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Summary: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 ≥ d - 4 t + 5 3 + p - 1 , where d is the diameter of G and p is the number of connected components of G and 1 ≤ t ≤ 3 . For general powers of edge ideals we show that depth R / I t ≥ 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 .
ISSN:0925-9899
1572-9192
DOI:10.1007/s10801-015-0604-3