K-6 minors in 6-connected graphs of bounded tree-width

摘要

We prove that every sufficiently large 6-connected graph of bounded tree-width either has a K-6 minor, or has a vertex whose deletion makes the graph planar. This is a step toward proving that the same conclusion holds for all sufficiently large 6-connected graphs. Jorgensen conjectured that it holds for all 6-connected graphs. (C) 2017 The Authors. Published by Elsevier Inc.