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Topological Minor


A graph H is called a topological minor, also known as a homeomorphic subgraph, of a graph G if a graph subdivision of H is isomorphic to a subgraph of G.

Every topological minor is also a graph minor, but the reverse is not necessarily true.

The subgraph homeomorphism problem consists of finding a homeomorphic image of a pattern graph H in an input graph G.


See also

Forbidden Homeomorphic Subgraph, Graph Minor, Graph Subdivision, Homeomorphic Graphs, Kuratowski's Theorem

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References

Diestel, R. Graph Theory, 3rd ed. Berlin, New York: Springer-Verlag, 2005.LaPaigh, A. S. and Rivest, R. L. "The Subgraph Homeomorphism Problem" J. Computer Sys. Sci. 20, 133-149, 1980.

Cite this as:

Weisstein, Eric W. "Topological Minor." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/TopologicalMinor.html

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