Collectanea Mathematica

, Volume 63, Issue 3, pp 361–374 | Cite as

Associated primes of powers of edge ideals

  • José Martínez-Bernal
  • Susan Morey
  • Rafael H. Villarreal


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 \({\overline{I^i}}\) 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.


Associated primes Edge-ideal Integral closure Perfect matching Analytic spread 

Mathematics Subject Classification (2000)

Primary 13C13 Secondary 13A30 13F55 05C25 05C75 


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Copyright information

© Universitat de Barcelona 2011

Authors and Affiliations

  • José Martínez-Bernal
    • 1
  • Susan Morey
    • 2
  • Rafael H. Villarreal
    • 1
  1. 1.Departamento de MatemáticasCentro de Investigación y de Estudios Avanzados del IPNMexico CityMexico
  2. 2.Department of MathematicsTexas State UniversitySan MarcosUSA

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