Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Squarefree monomial ideals that fail the persistence property and
  non-increasing depth   In a recent work, Kaiser, Stehl\'ik and \v{S}krekovski provide a family of
critically 3-chromatic graphs whose expansions do not result in critically
4-chromatic graphs, and thus give counterexamples to a conjecture of Francisco,
Ha and Van Tuyl. The cover ideal of the smallest member of this family also
gives a counterexample to the persistence and non-increasing depth properties.
In this paper, we show that the cover ideals of all members of their family of
graphs indeed fail to have the persistence and non-increasing depth properties.

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The categories of this paper are: astro-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: adap-org
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The categories of this paper are: eess
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-th
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The categories of this paper are: econ
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The categories of this paper are: hep-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: nlin
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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: alg-geom
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The categories of this paper are: supr-con