K_5 subdivisions in 5-connected nonplanar graphs

Series: 
Graph Theory Seminar
Thursday, April 23, 2009 - 12:05
1.5 hours (actually 80 minutes)
Location: 
Skiles 255
,  
School of Mathematics, Georgia Tech
Organizer: 
A well know theorem of Kuratowski states that a graph is planar graph iff it contains no TK_5 or TK_{3,3}. In 1970s Seymour conjectured that every 5-connected nonplanar graph contains a TK_5. In the talk we will discuss several special cases of the conjecture, for example the graphs containing K_4^- (K_4 withour an edge). A related independent paths theorem also will be covered.