Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hamiltonian cycles in some family of cubic $3$-connected plane graphs   Barnette conjectured that all cubic $3$-connected plane graphs with maximum
face size at most $6$ are hamiltonian. We provide a method of construction of a
hamiltonian cycle (in dual terms) in an arbitrary cubic, $3$-connected plane
graph possessing such a face $g$ that every face incident with $g$ has at most
$5$ edges and every other face has at most $6$ edges.

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The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex