Graph Isomorphism for (H1,H2)-Free Graphs: An Almost Complete Dichotomy.

We resolve the computational complexity of Graph Isomorphism for classes of graphs characterized by two forbidden induced subgraphs H 1 and H 2 for all but six pairs (H 1 , H 2) . Schweitzer had previously shown that the number of open cases was finite, but without specifying the open cases. Grohe and Schweitzer proved that Graph Isomorphism is polynomial-time solvable on graph classes of bounded clique-width. Our work combines known results such as these with new results. By exploiting a relationship between Graph Isomorphism and clique-width, we simultaneously reduce the number of open cases for boundedness of clique-width for (H 1 , H 2) -free graphs to five. [ABSTRACT FROM AUTHOR]