# Fixed-Parameter Tractable Canonization and Isomorphism Test for Graphs of Bounded Treewidth

@article{Lokshtanov2014FixedParameterTC, title={Fixed-Parameter Tractable Canonization and Isomorphism Test for Graphs of Bounded Treewidth}, author={Daniel Lokshtanov and Marcin Pilipczuk and Michał Pilipczuk and Saket Saurabh}, journal={2014 IEEE 55th Annual Symposium on Foundations of Computer Science}, year={2014}, pages={186-195} }

We give a fixed-parameter tractable algorithm that, given a parameter k and two graphs G<sub>1</sub>, G<sub>2</sub>, either concludes that one of these graphs has treewidth at least k, or determines whether G<sub>1</sub> and G<sub>2</sub> are isomorphic. The running time of the algorithm on an n-vertex graph is 2<sup>O(k5 log k)</sup> · n<sup>5</sup>, and this is the first fixed-parameter algorithm for Graph Isomorphism parameterized by treewidth. Our algorithm in fact solves the more general…

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