Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The number of Gallai k-colorings of complete graphs   An edge coloring of the $n$-vertex complete graph, $K_n$, is a Gallai
coloring if it does not contain any rainbow triangle, that is, a triangle whose
edges are colored with three distinct colors. We prove that for $n$ large and
every $k$ with $k\le 2^{n/4300}$, the number of Gallai colorings of $K_n$ that
use at most $k$ given colors is $(\binom{k}{2}+o_n(1))\,2^{\binom{n}{2}}$. Our
result is asymptotically best possible and implies that, for those $k$, almost
all Gallai $k$-colorings use only two colors. However, this is not true for $k
\ge \Omega (2^{2n})$.

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The categories of this paper are: math-ph
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The categories of this paper are: eess
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ex
1
The categories of this paper are: cs
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
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The categories of this paper are: chem-ph
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The categories of this paper are: mtrl-th
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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: chao-dyn
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The categories of this paper are: acc-phys