On the isomorphism of graphs with few P4s

Abstract

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 and the leaves are basic graphs with a simple structure. The paper extends and generalizes results on cographs, P4-reducible graphs, and P4-sparse graphs.