Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Three-coloring triangle-free graphs on surfaces IV. Bounding face sizes
  of 4-critical graphs   Let G be a 4-critical graph with t triangles, embedded in a surface of genus
g. Let c be the number of 4-cycles in G that do not bound a 2-cell face. We
prove that the sum of lengths of (>=5)-faces of G is at most linear in g+t+c-1.

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The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas