Some results on Castelnuovo-Mumford regularity of graph ideals and their powers

Let G be a nite simple graph and I(G) denote the corresponding edge ideal. The purpose of this talk is rst of all to review a number of recent studies of the Castelnuovo-Mumford regularity of edge ideals and their powers, then we give new upper bound for the regularity of the quotient ring R=I(G)s in terms of combinatorial data from associated graphs.

Keywords:

Edge ideal , Castelnuovo-Mumford regularity , Matching number