Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Outerplanar Tur\'{a}n numbers of cycles and paths   A graph is outerplanar if it can be embedded in a plane such that all
vertices lie on its outer face. The outerplanar Tur\'{a}n number of a given
graph $H$, denoted by ${\rm ex}_{\mathcal{OP}}(n,H)$, is the maximum number of
edges over all outerplanar graphs on $n$ vertices which do not contain a copy
of $H$. In this paper, the outerplanar Tur\'{a}n numbers of cycles and paths
are completely determined.

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The categories of this paper are: funct-an
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The categories of this paper are: nucl-th
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The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
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The categories of this paper are: econ
7
The categories of this paper are: hep-th
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The categories of this paper are: acc-phys
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: nlin
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The categories of this paper are: hep-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: cmp-lg