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
or utility graph as a graph minor. The
following table summarizes some simple graph families which have forbidden minor
obstructions.