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Forbidden Induced Subgraph


A graph is a forbidden (vertex-)induced subgraph if its presence as a vertex-induced subgraph of a given graph means it is not a member of some family of graphs. For example, a claw-free graph is a graph that does not contain the claw graph K_(1,3) as a vertex-induced subgraph.

More generally, there may be a family of vertex-induced subgraphs whose presence characterizes if a given graph has some property. For example, a simple graph is a line graph iff it does not contain one of the 9 Beineke graphs as a vertex-induced subgraph. The following table summarizes some graph families which have forbidden induced subgraph obstructions.


See also

Claw-Free Graph, Forbidden Minor, Forbidden Subgraph

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Cite this as:

Weisstein, Eric W. "Forbidden Induced Subgraph." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ForbiddenInducedSubgraph.html

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