Chapter

Parameterized and Exact Computation

Volume 7535 of the series Lecture Notes in Computer Science pp 218-230

On Tractable Parameterizations of Graph Isomorphism

  • Adam BoulandAffiliated withLancaster UniversityMassachusetts Institute of Technology
  • , Anuj DawarAffiliated withLancaster UniversityUniversity of Cambridge
  • , Eryk KopczyńskiAffiliated withCarnegie Mellon UniversityUniversity of Warsaw

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Abstract

The fixed-parameter tractability of graph isomorphism is an open problem with respect to a number of natural parameters, such as tree-width, genus and maximum degree. We show that graph isomorphism is fixed-parameter tractable when parameterized by the tree-depth of the graph. We also extend this result to a parameter generalizing both tree-depth and max-leaf-number by deploying new variants of cops-and-robbers games.