Resumen de 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 ??⎯⎯⎯⎯⎯ 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.