有向图中的循环邻域
Cyclic Neighborhoods in Digraphs
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中文总结 AI 辅助
针对满足任意顶点邻域非循环的有向图，证明强连通时边数下界为7n/3、强2-连通时为8n/3，两个下界均为最优。
中文摘要 AI 辅助
设D为阶数n、边数m的有向图，满足其任意顶点的出邻域或入邻域均非循环。我们证明：若D是强连通的，则m≥7n/3；若D是强2-连通的，则m≥8n/3，且两个结果均为最优。
英文摘要
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.
