K₆ minors in large 6-connected graphs

2012/03/09 by Kawarabayashi, Ken-ichi, Norine, Serguei, Thomas, Robin +1
#Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics

paper · doi:10.48550/arxiv.1203.2192

Abstract

Jorgensen conjectured that every 6-connected graph with no K₆ minor has a vertex whose deletion makes the graph planar. We prove the conjecture for all sufficiently large graphs.

Related

• K₆ minors in 6-connected graphs of bounded tree-width
• Extremal results regarding K₆-minors in graphs of girth at least 5
• Graphs without large K_2,n-minors
• Every graph with no K₇^\vee-minor is 6-colorable
• Every graph with no K₉^-6 minor is 8-colorable