For example, the graph

* | *--*--* | *is a minor of

* /| *-*--*-*-* |/ *(the outer edges are removed, the long middle edge is contracted).

The relation "being a minor of" is a partial order on the isomorphism classes of graphs.

Many classes of graphs can be characterized by "forbidden minors": a graph belongs to the class if and only if it does not have a minor from a certain specified list. The best-known example is Kuratowski's theorem for the characterization of planar graphs. The general situation is described by the Robertson-Seymour theorem.

Another deep result by Robertson-Seymour states that if any infinite list *G*_{1}, *G*_{2},... of finite graphs is given, then there always exists two indices *i* < *j* such that *G*_{i} is a minor of *G*_{j}.

In linear algebra, there is a different unrelated meaning of the word