A forbidden topological minor (also known as a forbidden homeomorphic subgraph) for a family of graphs is a graph 
such that no member of the family contains a graph
subdivision of 
as a subgraph. For example, Kuratowski's theorem states that a finite undirected graph is planar iff it contains neither the complete
graph 
nor the utility graph 
as a topological minor.
The following table summarizes known forbidden topological minor obstructions for several embeddability families. The torus row includes planar graphs and records a partial list (Myrvold and Woodcock 2018, p. 10).
| family | known obstructions |
| planar graph |  ,
 |
| projective planar graph | 103 graphs |
| graphs with a torus graph embedding | 
graphs |
