Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Zigzag Structure of Simple Two-faced Polyhedra   A zigzag in a plane graph is a circuit of edges, such that any two, but no
three, consecutive edges belong to the same face. A railroad in a plane graph
is a circuit of hexagonal faces, such that any hexagon is adjacent to its
neighbors on opposite edges. A graph without a railroad is called tight. We
consider the zigzag and railroad structures of general 3-valent plane graph
and, especially, of simple two-faced polyhedra, i.e., 3-valent 3-polytopes with
only $a$-gonal and $b$-gonal faces, where $3 \le a < b \le 6$; the main cases
are $(a,b)=(3,6)$, $(4,6)$ and $(5,6)$ (the fullerenes).
  We completely describe the zigzag structure for the case $(a,b)$=$(3,6)$. For
the case $(a,b)$=$(4,6)$ we describe symmetry groups, classify all tight graphs
with simple zigzags and give the upper bound 9 for the number of zigzags in
general tight graphs. For the remaining case $(a,b)$=$(5,6)$ we give a
construction realizing a prescribed zigzag structure.

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The categories of this paper are: q-fin
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The categories of this paper are: econ
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
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The categories of this paper are: solv-int
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The categories of this paper are: eess
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The categories of this paper are: math-ph
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
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The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
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The categories of this paper are: hep-ex
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The categories of this paper are: quant-ph