Powers of Ideals Associated to $(C_4,2K_2)$-free Graphs

Let $G$ be a $(C_4,2K_2)$-free graph with edge ideal $I(G)\subset \Bbbk[x_1,\dots , x_n]$\mathrm{.}Weshowthat$I(G)^s$haslinearresolutionforevery$s\geq 2$\mathrm{.}Also,weshowthateverypowerofthevertexcoveridealof$G$ has linear quotients. As a result, we describe the Castelnuovo-Mumford regularity of powers of $I(G{)}^{\vee }$ in terms of the maximum degree of $G$.