论文标题
在图形的边缘理想的符号力量深度上
On the depth of symbolic powers of edge ideals of graphs
论文作者
论文摘要
假设$ g $是一个带有edge gibles $ i（g）$和星形包装编号$α_2（g）$的图。我们表示$ i（g）$ y（g）^{（s）} $的$ s $ th符号功率。结果表明，不等式$ {\ rm depth} s/（i（g）^{（s）}）\ geqα_2（g）-s+1 $对于每个和弦图$ g $和每个整数$ s $ s \ s \ geq 1 $都是正确的。此外，事实证明，对于任何图$ g $，我们都有$ {\ rm depth} s/（i（g）^{（2）}）\ geqα_2（g）-1 $。
Assume that $G$ is a graph with edge ideal $I(G)$ and star packing number $α_2(G)$. We denote the $s$-th symbolic power of $I(G)$ by $I(G)^{(s)}$. It is shown that the inequality ${\rm depth} S/(I(G)^{(s)})\geq α_2(G)-s+1$ is true for every chordal graph $G$ and every integer $s\geq 1$. Moreover, it is proved that for any graph $G$, we have ${\rm depth} S/(I(G)^{(2)})\geq α_2(G)-1$.
