English

The minimal nonplanar strong digraphs

Combinatorics 2025-03-11 v1

Abstract

Kuratowski's theorem says that the minimal (under subgraph containment) graphs that are not planar are the subdivisions of K5K_5 and of K3,3K_{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.

Keywords

Cite

@article{arxiv.2503.06718,
  title  = {The minimal nonplanar strong digraphs},
  author = {Stephen Bartell and Paul Seymour},
  journal= {arXiv preprint arXiv:2503.06718},
  year   = {2025}
}
R2 v1 2026-06-28T22:13:04.212Z