Minors of plane digraphs
Combinatorics
2026-04-02 v1
Abstract
A digraph is a ``semi-strong minor'' of another, , if a subdivision of can be obtained from a subdigraph of 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 , all plane digraphs not containing as a semi-strong minor have bounded width, while plane digraphs in general have unbounded width.
Keywords
Cite
@article{arxiv.2604.00833,
title = {Minors of plane digraphs},
author = {Maria Chudnovsky and Paul Seymour},
journal= {arXiv preprint arXiv:2604.00833},
year = {2026}
}