We study a graph transformation (defined by Seidel) called switching which, given a graph G = (V, E) and a subset W⊆V of its vertices, builds a new graph by exchanging the cocycle linking W to V⧹W with its complement. Switching is an equivalence relation and the associated equivalence classes are called switching classes. A switching class is perfect if it contains only perfect graphs. We show that a switching class is perfect if and only if some graph in the class is P4-free, and that whether a graph belongs to such a class can be determined in polynomial time. We also show that a graph belongs to a perfect switching class if and only if it contains no C5, bull, gem or anti-gem as an induced subgraph.
