Circle Graph Obstructions

A circle graph is an intersection graph of finitely many chords of a circle. A local complementation of a simple graph G at one of its vertices v is the operation which replaces the subgraph of G induced by the neighborhood of v by its complement. Two graphs are locally equivalent if one of them is obtained from the other one by successive local complementations. THEOREM. A simple graph G is a circle graph if and only if no graph locally equivalent to G has an induced subgraph isomorphic to one of the graphs depicted in Figure 3.