Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Beraha number $B_{10}$ is a chromatic root   This note exhibits graphs whose chromatic polynomials have the Beraha number
$B_{10} = (5 + \sqrt{5})/2$ as a root. It was previously known that no other
non-integer Beraha number is a chromatic root, and so these examples complete
the determination of precisely which Beraha numbers can be chromatic roots.

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The categories of this paper are: econ
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The categories of this paper are: dg-ga
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The categories of this paper are: chem-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: plasm-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: nlin
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The categories of this paper are: acc-phys
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The categories of this paper are: cs
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The categories of this paper are: solv-int
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The categories of this paper are: physics
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The categories of this paper are: q-fin
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The categories of this paper are: q-alg
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The categories of this paper are: adap-org
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The categories of this paper are: astro-ph
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The categories of this paper are: patt-sol