Abstract
We show that several reducibility notions coincide when applied to the Graph Isomorphism (GI) problem. In particular we show that if a set is many-one logspace reducible to GI, then it is in fact many-one AC0 reducible to GI. For the case of Turing reducibilities we show that for any k > 0 an NCk+1 reduction to GI can be transformed into an ACk reduction to the same problem. © Springer-Verlag Berlin Heidelberg 2007.
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Torán, J. (2007). Reductions to graph isomorphism. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4855 LNCS, pp. 158–167). Springer Verlag. https://doi.org/10.1007/978-3-540-77050-3_13
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