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Homesubdivision

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# 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, $TC_{4}$ 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 *Modern Graph Theory* by Béla Bollobás, published by Springer-Verlag New York, Inc., 1998.

Related:

Homeomorphic, Realization

Synonym:

topological minor

Type of Math Object:

Definition

Major Section:

Reference

## Mathematics Subject Classification

05C99*no label found*

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