A graph is said to be a subdivision, or topological minor of a graph , or a topological graph if is obtained from by subdividing some of the edges, that is, by replacing the edges by paths having at most their endvertices in common. We often use for a topological graph.

Thus, denotes any member of a large family of graphs; for example, is an arbitrary cycle of length at least 4. For any graph , the spaces (denoting the realization of G) and are homeomorphic.

Adapted with permission of the author from Modern Graph Theory by Béla Bollobás, published by Springer-Verlag New York, Inc., 1998.