Emergent Mind

Graph Isomorphism for $(H_1,H_2)$-free Graphs: An Almost Complete Dichotomy

(1811.12252)
Published Nov 29, 2018 in cs.DM and math.CO

Abstract

We resolve the computational complexity of Graph Isomorphism for classes of graphs characterized by two forbidden induced subgraphs $H1$ and $H2$ for all but six pairs $(H1,H2)$. 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 $(H1,H2)$-free graphs to five.

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