Minors of plane digraphs
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911559851180032 |
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| author | Chudnovsky, Maria Seymour, Paul |
| author_facet | Chudnovsky, Maria Seymour, Paul |
| contents | A digraph $H$ is a ``semi-strong minor'' of another, $G$, if a subdivision of $H$ can be obtained from a subdigraph of $G$ by contracting strongly-connected subdigraphs to single vertices. We will define a width measure of ``plane'' digraphs (that is, drawn in the plane) based on a kind of branch-composition, and show that for every plane digraph $H$, all plane digraphs not containing $H$ as a semi-strong minor have bounded width, while plane digraphs in general have unbounded width. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_00833 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Minors of plane digraphs Chudnovsky, Maria Seymour, Paul Combinatorics A digraph $H$ is a ``semi-strong minor'' of another, $G$, if a subdivision of $H$ can be obtained from a subdigraph of $G$ by contracting strongly-connected subdigraphs to single vertices. We will define a width measure of ``plane'' digraphs (that is, drawn in the plane) based on a kind of branch-composition, and show that for every plane digraph $H$, all plane digraphs not containing $H$ as a semi-strong minor have bounded width, while plane digraphs in general have unbounded width. |
| title | Minors of plane digraphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2604.00833 |