The Kelmans-Seymour conjecture II: special separations (5-separations containing a triangle)

Graph Theory Seminar
Friday, February 5, 2016 - 3:05pm
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^-. 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 whose cut contains a triangle. Results will be used in subsequently to prove the Kelmans-Seymour conjecture.