论文标题
关于涵盖图的理想的符号能力的最小自由分辨率
On the minimal free resolution of symbolic powers of cover ideals of graphs
论文作者
论文摘要
对于任何图$ g $，假设$ j（g）$是$ g $的封面理想。令$ j（g）^{（k）} $表示$ j（g）$的$ k $ th符号功率。我们用$ j（g）^{（k）} $的属性表征所有图表$ g $，对于某些（等效地，所有）整数$ k \ geq 2 $具有线性分辨率。此外，可以证明，对于任何图$ g $，序列$ \ big（{\ rm reg}（j（g）^{（k）}）\ big）_ {k = 1}^{\ infty} $是无eCreasing的。此外，当$ g $是无爪图的无混合时，我们计算$ j（g）^{（k）} $的最小发电机的最小生成器。
For any graph $G$, assume that $J(G)$ is the cover ideal of $G$. Let $J(G)^{(k)}$ denote the $k$th symbolic power of $J(G)$. We characterize all graphs $G$ with the property that $J(G)^{(k)}$ has a linear resolution for some (equivalently, for all) integer $k\geq 2$. Moreover, it is shown that for any graph $G$, the sequence $\big({\rm reg}(J(G)^{(k)})\big)_{k=1}^{\infty}$ is nondecreasing. Furthermore, we compute the largest degree of minimal generators of $J(G)^{(k)}$ when $G$ is either an unmixed of a claw-free graph.
