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

Thus, TG denotes any member of a large family of graphs; for example, TC4 is an arbitrary cycle of length at least 4. For any graph G, the spaces R(G) (denoting the realization of G) and R(TG) are homeomorphic.

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

Title subdivision
Canonical name Subdivision
Date of creation 2013-03-22 12:31:51
Last modified on 2013-03-22 12:31:51
Owner CWoo (3771)
Last modified by CWoo (3771)
Numerical id 5
Author CWoo (3771)
Entry type Definition
Classification msc 05C99
Synonym topological minor
Related topic Homeomorphic
Related topic Realization