English

The excluded minor structure theorem with planarly embedded wall

Combinatorics 2009-10-17 v3

Abstract

A graph is nearly embedded in a surface if it consists of graph G0G_0 that is embedded in the surface, together with a bounded number of vortices having no large transactions. It is shown that every large wall (or grid minor) in a nearly embedded graph, many rows of which intersect the embedded subgraph G0G_0 of the near-embedding, contains a large subwall that is planarly embedded within G0G_0. This result provides some hidden details needed for a strong version of the Robertson and Seymour's excluded minor theorem as presented in [K. Kawarabayashi, B. Mohar, Some recent progress and applications in graph minor theory, Graphs Combin. 23 (2007) 1-46].

Keywords

Cite

@article{arxiv.0909.4329,
  title  = {The excluded minor structure theorem with planarly embedded wall},
  author = {Bojan Mohar},
  journal= {arXiv preprint arXiv:0909.4329},
  year   = {2009}
}
R2 v1 2026-06-21T13:49:47.577Z