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 
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.
| family | obstruction(s) |
| chordal graph | cycle graphs  for  , 5, ... |
| claw-free graph | claw graph  |
| line graph | Beineke graphs |
line graph with  | Metelsky graphs |
| split graph |  ,  ,  |
| triangle-free graph | triangle graph  |
| unswitchable graph |  ,
 ,
 |
