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arXiv · 2411.09791

Generating strongly 2-connected digraphs

Meike Hatzel·Stephan Kreutzer·Evangelos Protopapas·Florian Reich·Giannos Stamoulis·Sebastian Wiederrecht
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Abstract

We prove that there exist four operations such that given any two strongly $2$-connected digraphs $H$ and $D$ where $H$ is a butterfly-minor of $D$, there exists a sequence $D_0,\dots, D_n$ where $D_0=H$, $D_n=D$ and for every $0\leq i\leq n-1$, $D_i$ is a strongly $2$-connected butterfly-minor of $D_{i+1}$ which is obtained by a single application of one of the four operations. As a consequence of this theorem, we obtain that every strongly $2$-connected digraph can be generated from a concise family of strongly $2$-connected digraphs by using these four operations.

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Meike Hatzel, Stephan Kreutzer, Evangelos Protopapas, Florian Reich, Giannos Stamoulis, Sebastian Wiederrecht. 2024-11-14. Generating strongly 2-connected digraphs. https://arxiv.org/abs/2411.09791

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