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Induced Matchings and the v-Number of Graded Ideals

Author

Listed:
  • Gonzalo Grisalde

    (Departamento de Matemáticas, Centro de Investigación y de Estudios Avanzados del IPN, Apartado Postal 14-740, Mexico City 07000, Mexico)

  • Enrique Reyes

    (Departamento de Matemáticas, Centro de Investigación y de Estudios Avanzados del IPN, Apartado Postal 14-740, Mexico City 07000, Mexico)

  • Rafael H. Villarreal

    (Departamento de Matemáticas, Centro de Investigación y de Estudios Avanzados del IPN, Apartado Postal 14-740, Mexico City 07000, Mexico)

Abstract

We give a formula for the v-number of a graded ideal that can be used to compute this number. Then, we show that for the edge ideal I ( G ) of a graph G , the induced matching number of G is an upper bound for the v-number of I ( G ) when G is very well-covered, or G has a simplicial partition, or G is well-covered connected and contains neither four, nor five cycles. In all these cases, the v-number of I ( G ) is a lower bound for the regularity of the edge ring of G . We classify when the induced matching number of G is an upper bound for the v-number of I ( G ) when G is a cycle and classify when all vertices of a graph are shedding vertices to gain insight into the family of W 2 -graphs.

Suggested Citation

  • Gonzalo Grisalde & Enrique Reyes & Rafael H. Villarreal, 2021. "Induced Matchings and the v-Number of Graded Ideals," Mathematics, MDPI, vol. 9(22), pages 1-16, November.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:22:p:2860-:d:676653
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