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Let $G$ be a $(C_4, 2K_2)$-free graph with edge ideal $I(G)\subset\Bbbk[x_1,\dots , x_n]$. We show that $I(G)^s$ has linear resolution for every$s\geq 2$. Also, we show that every power of the vertex cover ideal of $G$ haslinear quotients. As a result, we describe the Castelnuovo-Mumford regularityof powers of $I(G)^{\vee}$ in terms of the maximum degree of $G$.

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