Let be a finite simple graph and denote the corresponding edge ideal. We prove that if is a very well-covered graph then for all the regularity of is exactly , where denotes the induced matching number of .
"Linear polynomials for the regularity of powers of edge ideals of very well-covered graphs." J. Commut. Algebra 13 (1) 89 - 101, Spring 2021. https://doi.org/10.1216/jca.2021.13.89