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 , there is a finite list of graphs with the property that a graph embeds on a surface of genus Iff it does not contain, as a minor, any of the graphs on the list .

**References**

Fellows, M. R. ``The Robertson-Seymour Theorems: A Survey of Applications.'' *Comtemp. Math.* **89**, 1-18, 1987.

© 1996-9

1999-05-25