Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Oriented Chromatic Number of the Hexagonal Grid is 6   The oriented chromatic number of a directed graph $G$ is the minimum order of
an oriented graph to which $G$ has a homomorphism. The oriented chromatic
number $\chi_o({\cal F})$ of a graph family ${\cal F}$ is the maximum oriented
chromatic number over any orientation of any graph in ${\cal F}$. For the
family of hexagonal grids ${\cal H}_2$, Bielak (2006) proved that $5 \le
\chi_o({\cal H}_2) \le 6$. Here we close the gap by showing that $\chi_o({\cal
H}_2) \ge 6$.

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The categories of this paper are: mtrl-th
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The categories of this paper are: funct-an
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The categories of this paper are: adap-org
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: math-ph
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The categories of this paper are: dg-ga
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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: hep-th
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The categories of this paper are: nucl-th
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The categories of this paper are: stat
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The categories of this paper are: ao-sci
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The categories of this paper are: cmp-lg
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The categories of this paper are: patt-sol
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The categories of this paper are: cs