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.

claw-free graph | forbidden minor | forbidden subgraph