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Testing Isomorphism of Chordal Graphs of Bounded Leafage is Fixed-Parameter Tractable (Extended Abstract)

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Graph-Theoretic Concepts in Computer Science (WG 2022)

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Abstract

The computational complexity of the graph isomorphism problem is considered to be a major open problem in theoretical computer science. It is known that testing isomorphism of chordal graphs is polynomial-time equivalent to the general graph isomorphism problem. Every chordal graph can be represented as the intersection graph of some subtrees of a representing tree, and the leafage of a chordal graph is defined to be the minimum number of leaves in a representing tree for it. We prove that chordal graph isomorphism is fixed parameter tractable with leafage as parameter.

The full version of this paper is available on arXiv [2]. Roman Nedela was supported by GAČR 20-15576S and APVV-19-0308. Peter Zeman was supported by the Swiss National Science Foundation project PP00P2-202667. While at Department of Applied Mathematics, Faculty of Mathematics and Physics, Charles University, Peter Zeman was supported by GAČR 20-15576S.

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Notes

  1. 1.

    After posting our paper on the arXiv [2], we found a paper [7] containing an FPT algorithm testing isomorphism of T-graphs for every fixed tree T. This gives an alternative FPT algorithm for chordal graphs of leafage \(\ell \).

  2. 2.

    Note that the composition \(fGf^{-1}\) is defined from left to right.

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Authors and Affiliations

  1. The Institute of Mathematical Sciences (HBNI), Chennai, India

    Vikraman Arvind

  2. Faculty of Applied Sciences, University of West Bohemia, Pilsen, Czech Republic

    Roman Nedela

  3. V. A. Steklov Institue of Mathematics, Russian Academy of Sciences, St. Petersburg, Russia

    Ilia Ponomarenko

  4. Institut de mathématiques, Université de Neuchâtel, Neuchâtel, Switzerland

    Peter Zeman

Authors
  1. Vikraman Arvind
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  2. Roman Nedela
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  3. Ilia Ponomarenko
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  4. Peter Zeman
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Correspondence to Peter Zeman .

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Editors and Affiliations

  1. University of Ioannina, Ioannina, Greece

    Michael A. Bekos

  2. Universität Tübingen, Tübingen, Germany

    Michael Kaufmann

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Arvind, V., Nedela, R., Ponomarenko, I., Zeman, P. (2022). Testing Isomorphism of Chordal Graphs of Bounded Leafage is Fixed-Parameter Tractable (Extended Abstract). In: Bekos, M.A., Kaufmann, M. (eds) Graph-Theoretic Concepts in Computer Science. WG 2022. Lecture Notes in Computer Science, vol 13453. Springer, Cham. https://doi.org/10.1007/978-3-031-15914-5_3

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