Powers of ideals associated to (C4, 2K2)-free graphs

Abstract

Let G be a (C-4, 2K(2))-free graph with edge ideal I(G) subset of k[x(1), . . . , x(n)]. We show that I(G)(s) has linear resolution for every s >= 2. Also, we show that every power of the vertex cover ideal of G has linear quotients. As a result, we describe the Castelnuovo-Mumford regularity of powers of I(G)(v) in terms of the maximum degree of G. (C) 2018 Elsevier B.V. All rights reserved.