Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Triangle-free planar graphs with at most $64^{n^{0.731}}$ 3-colorings   Thomassen conjectured that triangle-free planar graphs have exponentially
many 3-colorings. Recently, he disproved his conjecture by providing examples
of such graphs with $n$ vertices and at most $2^{15n/\log_2 n}$ 3-colorings. We
improve his construction, giving examples of such graphs with at most
$64^{n^{log_{9/2} 3}}<64^{n^{0.731}}$ 3-colorings. We conjecture this exponent
is optimal.

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The categories of this paper are: q-bio
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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: plasm-ph
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The categories of this paper are: hep-lat
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: cmp-lg
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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: cond-mat
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ex
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The categories of this paper are: supr-con
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The categories of this paper are: nucl-th