subdivision (original) (raw)

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 T⁢G for a topological G graph.

Thus, T⁢G denotes any member of a large family of graphs; for example, T⁢C4 is an arbitrary cycle of length at least 4. For any graph G, the spaces R⁢(G) (denoting the realization of G) and R⁢(T⁢G) are homeomorphic.

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