Associated primes of powers of edge ideals

Let G be a graph and let I be its edge ideal. Our main result shows that the sets of associated primes of the powers of I form an ascending chain. It is known that the sets of associated primes of I i and stabilize for large i . We show that their corresponding stable sets are equal. To show our mai...

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Bibliographic Details
Published inCollectanea mathematica (Barcelona) Vol. 63; no. 3; pp. 361 - 374
Main Authors Martínez-Bernal, José, Morey, Susan, Villarreal, Rafael H.
Format Journal Article
LanguageEnglish
Published Milan Springer Milan 01.09.2012
Subjects
Algebra
Analysis
Applications of Mathematics
Geometry
Mathematics
Mathematics and Statistics
Edge-ideal
05C75
Associated primes
Analytic spread
Secondary 13A30
Integral closure
05C25
Perfect matching
Primary 13C13
13F55
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Summary:Let G be a graph and let I be its edge ideal. Our main result shows that the sets of associated primes of the powers of I form an ascending chain. It is known that the sets of associated primes of I i and stabilize for large i . We show that their corresponding stable sets are equal. To show our main result we use a classical result of Berge from matching theory and certain notions from combinatorial optimization.
ISSN:0010-0757
2038-4815
DOI:10.1007/s13348-011-0045-9