subdivision

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, $T{C}_4$ 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