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Durham University

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Publication details

Bonamy, M., Bousquet, N., Dabrowski, K.K., Johnson, M., Paulusma, D. & Pierron, T. (2021). Graph isomorphism for (H1,H2)-free graphs: an almost complete dichotomy. Algorithmica 83(3): 822-852.

Author(s) from Durham


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.