An upper bound for the regularity of powers of edge ideals

‎A recent result due to Ha and Van Tuyl proved that the Castelnuovo-Mumford regularity of the quotient ring R/I(G) is at most matching number of G‎, ‎denoted by match(G)‎. ‎In this paper‎, ‎we provide a generalization of this result for powers of edge ideals‎. ‎More precisely‎, ‎we show that for every graph G and every s≥1‎, ‎ reg(R‎/‎I(G)s)≤(2s−1)|E(G)|s−1match(G).