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Two graphs G, H are isomorphic if there is a relabeling of the vertices of G that produces H, and vice-versa. The graph isomorphism problem (GI) is to decide whether two given are isomorphic. In addition to its practical interest, it was identified by Karp in 1972 as having unknown complexity, is one of the few remaining natural candidates for an NP-intermediate problem, and led to the creation of the complexity class AM.

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Open problems related to Graph isomorphism

For the first question: Graph Isomorphism has been considered for at least the following parameters for which fixed-parameter tractability is still open. pathwidth / treewidth (see [2], has been ask …
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