ON THE DEPTH OF SYMBOLIC POWERS OF EDGE IDEALS OF GRAPHS
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Abstract 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$ .
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2019 ◽
Vol 18
(10)
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pp. 1950184
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2019 ◽
Vol 19
(10)
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pp. 2050184
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2012 ◽
Vol 49
(4)
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pp. 501-508
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