Induced Matchings and the v-Number of Graded Ideals

@article{Grisalde2021InducedMA,
  title={Induced Matchings and the v-Number of Graded Ideals},
  author={Gonzalo Grisalde and Enrique Reyes and Rafael H. Villarreal},
  journal={Mathematics},
  year={2021}
}
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… 

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