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arXiv · 2607.26606

Cyclic Neighborhoods in Digraphs

Thilo Hartel·Dieter Rautenbach
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Abstract

Let $D$ be a digraph of order $n$ and size $m$ with the property that no out-neighborhood or in-neighborhood of any vertex is acyclic. We show that, if $D$ is strongly connected, then $m\geq 7n/3$, and, if $D$ is strongly $2$-connected, then $m\geq 8n/3$. Both results are best-possible.

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Thilo Hartel, Dieter Rautenbach. 2026-07-29. Cyclic Neighborhoods in Digraphs. https://arxiv.org/abs/2607.26606

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