Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Planar graphs with the maximum number of induced 4-cycles or 5-cycles   For large $n$ we determine exactly the maximum numbers of induced $C_4$ and
$C_5$ subgraphs that a planar graph on $n$ vertices can contain. We show that
$K_{2,n-2}$ uniquely achieves this maximum in the $C_4$ case, and we identify
the graphs which achieve the maximum in the $C_5$ case. This extends work in a
paper by Hakimi and Schmeichel and a paper by Ghosh, Gy\H{o}ri, Janzer, Paulos,
Salia, and Zamora which together determine both maxima asymptotically.

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The categories of this paper are: hep-lat
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The categories of this paper are: solv-int
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The categories of this paper are: hep-th
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The categories of this paper are: econ
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The categories of this paper are: atom-ph
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The categories of this paper are: q-alg
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The categories of this paper are: nlin
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: plasm-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: eess