subdivisionSubdivision2002-03-07 13:47:212008-05-06 18:07:17Definition% this is the default PlanetMath preamble. as your knowledge
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% define commands hereA graph $H$ is said to be a \emph{subdivision}, or \emph{topological minor} of a graph $G$, or a \emph{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 \emph{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.
\footnotesize{Adapted with permission of the author from \emph{\PMlinkescapetext{Modern Graph Theory}} by B\'{e}la Bollob\'{a}s, published by Springer-Verlag New York, Inc., 1998.}