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arXiv · 2607.10036

On the Turán number of the directed path

Daniel P. Johnston·Cory Palmer·Amites Sarkar
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Abstract

In this note we determine the maximum number of arcs in a digraph on $n$ vertices that does not contain a length-$k$ directed path $\overrightarrow{P}_{k+1}$ for $n \geq 50k^6$. This improves a theorem of Zhou and Li [$\textit{Graphs Combin.}$ 39(3), 2023] who proved the result with a superexponential threshold on $n$.

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Daniel P. Johnston, Cory Palmer, Amites Sarkar. 2026-07-10. On the Turán number of the directed path. https://arxiv.org/abs/2607.10036

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