论文标题
图表的表征其边缘理想的较小力量具有线性无线分辨率
Characterization of graphs whose a small power of their edge ideals has a linear free resolution
论文作者
论文摘要
令$ i（g）$为简单的图形$ g $的优势。我们证明，$ i（g）^2 $具有线性免费分辨率，并且仅当$ g $不含差距和reg $ i（g）\ le 3 $时。同样，我们证明$ i（g）^3 $具有线性的免费分辨率，并且仅当$ g $不含间隙和reg $ i（g）\ le 4 $时。我们将这些特征从通用公式推导出无间隙图的边缘理想的规律性$$ {\ rm reg}（i（g）^s）= \ max（{\ rm reg} i（g） + s-1,2s），$ s = 2,3 $。
Let $I(G)$ be the edge ideal of a simple graph $G$. We prove that $I(G)^2$ has a linear free resolution if and only if $G$ is gap-free and reg$I(G) \le 3$. Similarly, we show that $I(G)^3$ has a linear free resolution if and only if $G$ is gap-free and reg$I(G) \le 4$. We deduce these characterizations from a general formula for the regularity of powers of edge ideals of gap-free graphs $${\rm reg}(I(G)^s) = \max({\rm reg} I(G) + s-1,2s),$$ for $s =2,3$.
