The Kelmans-Seymour conjecture I: Special Separations

Graph Theory Seminar
Wednesday, January 27, 2016 - 15:05
1 hour (actually 50 minutes)
Skiles 005
Math, GT
Seymour and, independently, Kelmans conjectured in the 1970s that every 5-connected nonplanar graph contains a subdivision of K_5. This conjecture was proved by Ma and Yu for graphs containing K_4^-, and an important step in their proof is to deal with a 5-separation in the graph with a planar side. In order to establish the Kelmans-Seymour conjecture for all graphs, we need to consider 5-separations and 6-separations with less restrictive structures. We will talk about special 5-separations and 6-separations, including those with an apex side. Results will be used in subsequently to prove the Kelmans-Seymour conjecture.