High Quality Content by WIKIPEDIA articles! A forbidden graph characterization is a method of specifying a family of graph, or hypergraph, structures. Families vary in the nature of what is forbidden. In general, a structure G is a member of a family if and only if a forbidden substructure is not contained in G. The forbidden substructure might simply be a subgraph, or a substructure from which one might derive (via, e.g., edge contraction or subdivision) that which is forbidden. Thus, the forbidden structure might be one of: