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arXiv · 1711.08535

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

Nursel Erey
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Abstract

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 $G$ 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 $G$.

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Nursel Erey. 2017-11-22. Powers of Ideals Associated to $(C_4, 2K_2)$-free Graphs. https://doi.org/10.1016/j.jpaa.2018.10.009

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