We present new classes of graphs for which the isomorphism problem can be solved in polynomial time. These graphs are characterized by containing - in some local sense - only a small number of induced paths of length three. As it turns out, every such graph has a unique tree representation: the internal nodes correspond to three types of graph operations, while the leaves are basic graphs with a simple structure. The paper extends and generalizes known results about cographs, P4-reducible graphs, and P4-sparse graphs. © 1998 Elsevier Science B.V. All rights reserved.
Babel, L., & Olariu, S. (1998). On the structure of graphs with few P4S. Discrete Applied Mathematics, 84(1–3), 1–13. https://doi.org/10.1016/S0166-218X(97)90120-7