Assume that G is a graph with edge ideal $I(G)$ and star packing number $\alpha _2(G)$ . We denote the sth symbolic power of $I(G)$ by $I(G)^{(s)}$ . It is shown that the inequality $ \operatorname {\mathrm {depth}} S/(I(G)^{(s)})\geq \alpha _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 $ \operatorname {\mathrm {depth}} S/(I(G)^{(2)})\geq \alpha _2(G)-1$ .

中文翻译：

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论边理想的象征力量的深度

假使，假设G是一个边缘理想的图 $I(G)$ 和星包装号 $\alpha_2(G)$ . 我们表示s的象征力量 $I(G)$ 经过 $I(G)^{(s)}$ . 表明不等式 $ \operatorname {\mathrm {深度}} S/(I(G)^{(s)})\geq \alpha _2(G)-s+1$ 对每个弦图都是正确的G和每一个整数 $s\geq 1$ . 此外，证明了对于任何图G， 我们有 $ \operatorname {\mathrm {深度}} S/(I(G)^{(2)})\geq \alpha _2(G)-1$ .