English

Minors of plane digraphs

Combinatorics 2026-04-02 v1

Abstract

A digraph HH is a ``semi-strong minor'' of another, GG, if a subdivision of HH can be obtained from a subdigraph of GG 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 HH, all plane digraphs not containing HH 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}
}
R2 v1 2026-07-01T11:48:09.691Z