Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sequentially Cohen-Macaulay Edge Ideals   Let G be a simple undirected graph on n vertices, and let I(G) \subseteq R =
k[x_1,...,x_n] denote its associated edge ideal. We show that all chordal
graphs G are sequentially Cohen-Macaulay; our proof depends upon showing that
the Alexander dual of I(G) is componentwise linear. Our result complements
Faridi's theorem that the facet ideal of a simplicial tree is sequentially
Cohen-Macaulay and implies Herzog, Hibi, and Zheng's theorem that a chordal
graph is Cohen-Macaulay if and only if its edge ideal is unmixed. We also
characterize the sequentially Cohen-Macaulay cycles and produce some examples
of nonchordal sequentially Cohen-Macaulay graphs.

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The categories of this paper are: stat
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The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
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The categories of this paper are: math-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: cond-mat
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The categories of this paper are: acc-phys
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The categories of this paper are: astro-ph
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The categories of this paper are: physics
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The categories of this paper are: supr-con
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The categories of this paper are: funct-an
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-th
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The categories of this paper are: plasm-ph