Editing Graph minor (section)

===Topological minors=== <!--Topological minor redirects here-->
A graph ''H'' is called a '''topological minor''' of a graph ''G'' if a [[Subdivision (graph theory)|subdivision]] of ''H'' is [[Graph isomorphism|isomorphic]] to a [[Glossary of graph theory#subgraph|subgraph]] of ''G''.<ref>{{Harvnb|Diestel|2005|p=20}}</ref> Every topological minor is also a minor. The converse however is not true in general (for instance the [[complete graph]] ''K''<sub>5</sub> in the [[Petersen graph]] is a minor but not a topological one), but holds for graph with maximum degree not greater than three.<ref>{{Harvnb|Diestel|2005|p=22}}</ref>

The topological minor relation is not a well-quasi-ordering on the set of finite graphs{{sfnp|Ding|1996}} and hence the result of Robertson and Seymour does not apply to topological minors. However it is straightforward to construct finite forbidden topological minor characterizations from finite forbidden minor characterizations by replacing every branch set with ''k'' outgoing edges by every tree on ''k'' leaves that has down degree at least two.