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Graph Isomorphism for (H1,H2)-free graphs: An Almost Complete Dichotomy

Bonamy, M. and Bousquet, N. and Dabrowski, K.K. and Johnson, M. and Paulusma, D. and Pierron, T. (2021) 'Graph Isomorphism for (H1,H2)-free graphs: An Almost Complete Dichotomy.', Algorithmica., 83 (3). pp. 822-852.


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.

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Date accepted:07 July 2020
Date deposited:14 July 2020
Date of first online publication:05 August 2020
Date first made open access:12 August 2020

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