Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Marked Groups with Isomorphic Cayley Graphs but Different Borel
  Combinatorics   We construct pairs of marked groups with isomorphic Cayley graphs but
different Borel chromatic numbers for the free parts of their shift graphs.
This answers a question of Kechris and Marks. We also show that these graphs
have different Baire measurable and measure chromatic numbers, answering
analogous versions of the question.

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The categories of this paper are: bayes-an
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The categories of this paper are: chem-ph
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The categories of this paper are: funct-an
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The categories of this paper are: acc-phys
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The categories of this paper are: math-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: supr-con
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The categories of this paper are: alg-geom
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The categories of this paper are: stat
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The categories of this paper are: q-bio
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-lat
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The categories of this paper are: econ
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-alg
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The categories of this paper are: ao-sci