Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Planar graphs have bounded nonrepetitive chromatic number   A colouring of a graph is "nonrepetitive" if for every path of even order,
the sequence of colours on the first half of the path is different from the
sequence of colours on the second half. We show that planar graphs have
nonrepetitive colourings with a bounded number of colours, thus proving a
conjecture of Alon, Grytczuk, Haluszczak and Riordan (2002). We also generalise
this result for graphs of bounded Euler genus, graphs excluding a fixed minor,
and graphs excluding a fixed topological minor.

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The categories of this paper are: quant-ph
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin
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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: nlin
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The categories of this paper are: bayes-an
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The categories of this paper are: q-bio
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The categories of this paper are: chao-dyn
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The categories of this paper are: solv-int