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homeomorphism (Definition)

We say that a graph $ G$ is homeomorphic to graph $ H$ if the realization $ R(G)$ of $ G$ is topologically homeomorphic to $ R(H)$ or, equivalently, $ G$ and $ H$ have isomorphic subdivisions.

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



"homeomorphism" is owned by digitalis.
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See Also: subdivision, realization of a graph
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Cross-references: subdivisions, isomorphic, homeomorphic, graph
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This is version 3 of homeomorphism, born on 2002-03-07, modified 2002-07-17.
Object id is 2773, canonical name is Homeomorphic.
Accessed 5538 times total.

Classification:
AMS MSC: 05C99 (Combinatorics :: Graph theory :: Miscellaneous)
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