Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Note on 3-Choosability of Planar Graphs with Maximum Degree 4   Deciding whether a planar graph (even of maximum degree $4$) is $3$-colorable
is NP-complete. Determining subclasses of planar graphs being $3$-colorable has
a long history, but since Gr\"{o}tzsch's result that triangle-free planar
graphs are such, most of the effort was focused to solving Havel's and
Steinberg's conjectures. In this paper, we prove that every planar graph of
maximum degree $4$ obtained as a subgraph of the medial graph of any bipartite
plane graph is $3$-choosable. These graphs are allowed to have close triangles
(even incident), and have no short cycles forbidden, hence representing an
entirely different class than the graphs inferred by the above mentioned
conjectures.

4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat