All minor-minimal apex obstructions with connectivity two

17 Aug 2018 · Adam S. Jobson, André E. Kézdy ·

A graph is an apex graph if it contains a vertex whose deletion leaves a planar graph. The family of apex graphs is minor-closed and so it is characterized by a finite list of minor-minimal non-members. The long-standing problem of determining this finite list of apex obstructions remains open. This paper determines the 133 minor-minimal, non-apex graphs that have connectivity two.