标题： 无间隙图和具有线性商的边理想幂 显示英文标题

标题： Gapfree graphs and powers of edge ideals with linear quotients

摘要： 设$G$是一个无间隙图，设$I(G)$是它的边理想。Nevo 和 Peeva 的一个开放猜想指出，$I(G)^q$对于$q\gg 0$有线性分解。我们研究了一个更强的猜想，即如果对于某个整数$q$，$I(G)^q$有线性商，则$I(G)^{q+1}$也有线性商。我们对该猜想给出了部分解答。 已知如果$G$不包含蟋蟀、钻石或$C_4$，则$I(G)^q$对$q \geq 2$有线性分解。 我们构造了一类不含间隙的图$G$，其中包含蟋蟀、钻石、$C_4$和$C_5$作为$G$的诱导子图，其中$I(G)^q$对$q \ge 2$有线性商。 显示英文摘要

摘要： Let $G$ be a gapfree graph and let $I(G)$ be its edge ideal. An open conjecture of Nevo and Peeva states that $I(G)^q$ has a linear resolution for $q\gg 0$. We investigate a stronger conjecture that if $I(G)^q$ has linear quotients for some integer $q$, then $I(G)^{q+1}$ also has linear quotients. We give a partial solution to this conjecture. It is known that if $G$ does not contain a cricket, a diamond, or a $C_4$, then $I(G)^q$ has a linear resolution for $q \geq 2$. We construct a family of gapfree graphs $G$ containing cricket, diamond, $C_4$ and $C_5$ as induced subgraphs of $G$ for which $I(G)^q$ has linear quotients for $q \ge 2$.