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arXiv · 2503.06718

The minimal nonplanar strong digraphs

Stephen Bartell·Paul Seymour
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Abstract

Kuratowski's theorem says that the minimal (under subgraph containment) graphs that are not planar are the subdivisions of $K_5$ and of $K_{3,3}$. Here we study the minimal (under subdigraph containment) strongly-connected digraphs that are not planar. We also find the minimal strongly-connected non-outerplanar digraphs and the minimal strongly-connected non-series-parallel digraphs.

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Stephen Bartell, Paul Seymour. 2025-03-09. The minimal nonplanar strong digraphs. https://arxiv.org/abs/2503.06718

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