forbidden minor graph

A graph is a forbidden minor if its presence as a graph minor of a given graph means it is not a member of some family of graphs. More generally, there may be a family of minors whose presence characterizes if a given graph has some property. For example, a planar graph is a graph that does not contain the complete graph K_5 or utility graph K_(3, 3) as a graph minor. The following table summarizes some simple graph families which have forbidden minor obstructions.

forbidden induced subgraph | forbidden subgraph | forbidden topological minor | Kuratowski's theorem | linklessly embeddable graph | outerplanar graph | planar graph | projective planar graph | Robertson-Seymour theorem | Wagner's theorem