The excluded minor structure theorem with planarly embedded wall

Abstract

A graph is "nearly embedded" in a surface if it consists of graph G0 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 G0 of the near-embedding, contains a large subwall that is planarly embedded within G0. This result provides some hidden details needed for a strong version of the Robertson and Seymour's excluded minor theorem as presented in [1]. Copyright © 2013 DMFA Slovenije.