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تسجيل مستخدم جديدThe Maximum Number of Paths of Length Four in a Planar Graph
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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 $n^{{lfloor{frac{k}{2}}rfloor}+1}$. In this paper we determine the asymptotic value of $f(n,P_4)$ and give conjectures for longer paths.
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