Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A new upper bound on the chromatic number of graphs with no odd $K_t$
  minor   Gerards and Seymour conjectured that every graph with no odd $K_t$ minor is
$(t-1)$-colorable. This is a strengthening of the famous Hadwiger's Conjecture.
Geelen et al. proved that every graph with no odd $K_t$ minor is $O(t\sqrt{\log
t})$-colorable. Using the methods the present authors and Postle recently
developed for coloring graphs with no $K_t$ minor, we make the first
improvement on this bound by showing that every graph with no odd $K_t$ minor
is $O(t(\log t)^{\beta})$-colorable for every $\beta > 1/4$.

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The categories of this paper are: nucl-ex
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The categories of this paper are: cs
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The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
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The categories of this paper are: eess
20
The categories of this paper are: acc-phys
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The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
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The categories of this paper are: q-fin
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The categories of this paper are: bayes-an
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The categories of this paper are: nlin
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The categories of this paper are: econ
4
The categories of this paper are: cond-mat
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The categories of this paper are: q-bio
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The categories of this paper are: patt-sol