K_6 minors in 6-connected graphs of bounded tree-width
  We prove that every sufficiently big 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 big 6-connected graphs. Jorgensen conjectured that it holds for all 6-connected graphs. 
Ken-ichi Kawarabayashi, Serguei Norine, Robin Thomas and Paul Wollan
math.CO cs.DM