The maximum number of paths of length four in a planar graph

@article{Ghosh2021TheMN,
  title={The maximum number of paths of length four in a planar graph},
  author={Debarun Ghosh and Ervin Gy{\"o}ri and Ryan R. Martin and Addisu Paulos and Nika Salia and Chuanqi Xiao and Oscar Zamora},
  journal={Discret. Math.},
  year={2021},
  volume={344},
  pages={112317}
}

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Let $f(n,H)$ denote the maximum number of copies of $H$ in an $n$-vertex planar graph. The order of magnitude of $f(n,P_k)$, where $P_k$ is a path of length $k$, is
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