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 
, 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 
.
