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The planar Tur\'an number of double star $S_{2,4}$
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abstract
Planar Tur\'an number $ex_{\mathcal{P}}(n,H)$ of $H$ is the maximum number of edges in an $n$-vertex planar graph which does not contain $H$ as a subgraph. Ghosh, Gy\H{o}ri, Paulos and Xiao initiated the topic of the planar Tur\'an number for double stars. In this paper, we prove that $ex_{\mathcal{P}}(n,S_{2,4})\leq \frac{31}{14}n$ for $n\geq 1$, and show that equality holds for infinitely many integers $n$.
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Cited by 1 Pith paper
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The Turan number of the balanced double star S_{n-1,n-1} in the hypercube Q_n
The paper claims ex(Q_n, S_{n-1,n-1}) equals 2^{n-3}(4n-3) for every n at least 3.
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