Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Iterated Arc Graphs   The arc graph $\delta(G)$ of a digraph $G$ is the digraph with the set of
arcs of $G$ as vertex-set, where the arcs of $\delta(G)$ join consecutive arcs
of $G$. In 1981, Poljak and R\"{o}dl characterised the chromatic number of
$\delta(G)$ in terms of the chromatic number of $G$ when $G$ is symmetric
(i.e., undirected). In contrast, directed graphs with equal chromatic numbers
can have arc graphs with distinct chromatic numbers. Even though the arc graph
of a symmetric graph is not symmetric, we show that the chromatic number of the
iterated arc graph $\delta^k(G)$ still only depends on the chromatic number of
$G$ when $G$ is symmetric.

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The categories of this paper are: mtrl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: econ
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The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: solv-int
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The categories of this paper are: nlin
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: eess
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The categories of this paper are: physics
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The categories of this paper are: supr-con
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The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th