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arXiv · 2102.10529

The Turan problems of directed paths and cycles in digraphs

Wenling Zhou·Binlong Li
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Abstract

Let $\overrightarrow{P_k}$ and $\overrightarrow{C_k}$ denote the directed path and the directed cycle of order $k$, respectively. In this paper, we determine the precise maximum size of $\overrightarrow{P_k}$-free digraphs of order $n$ as well as the extremal digraphs attaining the maximum size for large $n$. For all $n$, we also determine the precise maximum size of $\overrightarrow{C_k}$-free digraphs of order $n$ as well as the extremal digraphs attaining the maximum size. In addition, Huang and Lyu [\textit{Discrete Math. 343(5) 2020}] characterized the extremal digraphs avoiding an orientation of $C_4$. For all other orientations of $C_4$, we also study the maximum size and the extremal digraphs avoiding them.

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Wenling Zhou, Binlong Li. 2021-02-21. The Turan problems of directed paths and cycles in digraphs. https://arxiv.org/abs/2102.10529

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