Associated primes of powers of edge ideals

• Autores: José Martínez-Bernal, Susan Morey, Rafael H. Villarreal
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 63, Fasc. 3, 2012, págs. 361-374
• Idioma: inglés
• DOI: 10.1007/s13348-011-0045-9
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• Resumen

  • 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.