Matching numbers and the regularity of the Rees algebra of an edge ideal
arXiv:1905.02141
Abstract
The regularity of the Rees ring of the edge ideal of a finite simple graph is studied. We show that the matching number is a lower and matching number~ is an upper bound of the regularity, if the Rees algebra is normal. In general the induced matching number is a lower bound for the regularity, which can be shown by applying the squarefree divisor complex.