LINEAR POLYNOMIALS FOR THE REGULARITY OF POWERS OF EDGE IDEALS OF VERY WELL-COVERED GRAPHS

Let G be a finite simple graph and I (G) denote the corresponding edge ideal. We prove that if G is a very well-covered graph then for all s > 1 the regularity of I(G)s is exactly 2s + v(G) - 1, where v(G) denotes the induced matching number of G.