graph minor theorem

The Robertson-Seymour theorem, also called the graph minor theorem, is a generalization of the Kuratowski reduction theorem by Robertson and Seymour, which states that the collection of finite graphs is well-quasi-ordered by minor embeddability, from which it follows that Kuratowski's "forbidden minor" embedding obstruction generalizes to higher genus surfaces. Formally, for a fixed integer g>=0, there is a finite list of graphs L(g) with the property that a graph C embeds on a surface of genus g iff it does not contain, as a minor, any of the graphs on the list L.

forbidden minor | graph minor | Kuratowski's theorem