Regularity of symbolic powers of edge ideals of chordal graphs (Q2105770)

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scientific article; zbMATH DE number 7629558
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Regularity of symbolic powers of edge ideals of chordal graphs
scientific article; zbMATH DE number 7629558

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    Regularity of symbolic powers of edge ideals of chordal graphs (English)
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    8 December 2022
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    Let \(G\) be a chordal graph with edge ideal \(I(G)\) and induced matching number \(\nu(G)\). Denote by \(I(G)^{(s)}\) the symbolic power of \(I(G)\). The author of this article studies the Castelnuovo-Mumford regularity \(\operatorname{reg}(I(G)^{(s)})\), for which in a previous article [the author, Electron. J. Comb. 26, No. 2, Research Paper P2.10, 9 p. (2019; Zbl 1411.13014)] an upper bound was found. In this paper, the regularity is actually computed and shown to be equal to \(2s+\nu(G)-1\) for every integer \(s\geq 1\).
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    Castelnuovo-Mumford regularity
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    chordal graph
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    edge ideal
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    matching number
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    symbolic powers
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