The Kelmans-Seymour conjecture V: no contractible edges or triangles (first part)

Graph Theory Seminar
Wednesday, April 6, 2016 - 15:05
1 hour (actually 50 minutes)
Skiles 005
Math, GT
Let G be a 5-connected nonplanar graph. To show the Kelmans-Seymour conjecture, we keep contracting a connected subgraph on a special vertex z until the following happens: H does not contain K_4^-, and for any subgraph T of H such that z is a vertex in T and T is K_2 or K_3, H/T is not 5-connected. In this talk, we prove a lemma using the characterization of three paths with designated ends, which will be used in the proof of the Kelmans-Seymour conjecture.