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Graph Isomorphism Parameterized by Elimination Distance to Bounded Degree

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Parameterized and Exact Computation (IPEC 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8894))

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Abstract

A commonly studied means of parameterizing graph problems is the deletion distance from triviality [10], which counts vertices that need to be deleted from a graph to place it in some class for which efficient algorithms are known. In the context of graph isomorphism, we define triviality to mean a graph with maximum degree bounded by a constant, as such graph classes admit polynomial-time isomorphism tests. We generalise deletion distance to a measure we call elimination distance to triviality, based on elimination trees or tree-depth decompositions. We establish that graph canonisation, and thus graph isomorphism, is \(\mathsf {FPT}\) when parameterized by elimination distance to bounded degree, generalising results of Bouland et al. [2] on isomorphism parameterized by tree-depth.

Research supported in part by EPSRC grant EP/H026835, DAAD grant A/13/05456, and DFG project Logik, Struktur und das Graphenisomorphieproblem.

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Authors and Affiliations

  1. University of Cambridge Computer Laboratory, Cambridge, UK

    Jannis Bulian & Anuj Dawar

Authors
  1. Jannis Bulian
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  2. Anuj Dawar
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Correspondence to Jannis Bulian or Anuj Dawar .

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Editors and Affiliations

  1. Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Warsaw, Poland

    Marek Cygan

  2. University of Bergen, Bergen, Norway

    Pinar Heggernes

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Bulian, J., Dawar, A. (2014). Graph Isomorphism Parameterized by Elimination Distance to Bounded Degree. In: Cygan, M., Heggernes, P. (eds) Parameterized and Exact Computation. IPEC 2014. Lecture Notes in Computer Science(), vol 8894. Springer, Cham. https://doi.org/10.1007/978-3-319-13524-3_12

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  • DOI: https://doi.org/10.1007/978-3-319-13524-3_12

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