Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Incidence Chromatic Number of Toroidal Grids   An incidence in a graph $G$ is a pair $(v,e)$ with $v \in V(G)$ and $e \in
E(G)$, such that $v$ and $e$ are incident. Two incidences $(v,e)$ and $(w,f)$
are adjacent if $v=w$, or $e=f$, or the edge $vw$ equals $e$ or $f$. The
incidence chromatic number of $G$ is the smallest $k$ for which there exists a
mapping from the set of incidences of $G$ to a set of $k$ colors that assigns
distinct colors to adjacent incidences. In this paper, we prove that the
incidence chromatic number of the toroidal grid $T_{m,n}=C_m\Box C_n$ equals 5
when $m,n \equiv 0 \pmod 5$ and 6 otherwise.

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The categories of this paper are: chem-ph
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The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-th
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The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
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The categories of this paper are: q-alg
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The categories of this paper are: econ
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The categories of this paper are: plasm-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
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The categories of this paper are: funct-an
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The categories of this paper are: comp-gas