Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonrepetitively 3-colorable subdivisions of graphs with a logarithmic
  number of subdivisions per edge   We show that for every graph $G$ and every graph $H$ obtained by subdividing
each edge of $G$ at least $O(\log |V(G)|)$, $H$ is nonrepetitively 3-colorable.
In fact, we show that $O(\log \pi'(G))$ subdivisions per edge are enough, where
$\pi'(G)$ is the nonrepetitive chromatic index of $G$. This answers a question
of Wood and improves a similar result of Pezarski and Zmarz that stated the
existence of at least one 3-colorable division with a linear number of
subdivision vertices per edge.

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The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
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The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
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The categories of this paper are: quant-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga
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The categories of this paper are: supr-con
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The categories of this paper are: eess
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The categories of this paper are: funct-an
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The categories of this paper are: ao-sci