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Hamiltonicity Parameterized by Mim-Width Is (Indeed) Para-NP-Hard

Authors Benjamin Bergougnoux , Lars Jaffke

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LIPIcs.IPEC.2025.31.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation → Problems, reductions and completeness
  • Mathematics of computing → Graph algorithms
Keywords
  • Hamiltonian Path
  • Hamiltonian Cycle
  • Mim-Width
  • Para-NP-Hardness

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Abstract

We prove that Hamiltonian Path and Hamiltonian Cycle are NP-hard on graphs of linear mim-width 26, even when a linear order of the input graph with mim-width 26 is provided together with input. This fills a gap left by a broken proof of the para-NP-hardness of Hamiltonicity problems parameterized by mim-width.

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Benjamin Bergougnoux and Lars Jaffke. Hamiltonicity Parameterized by Mim-Width Is (Indeed) Para-NP-Hard. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 31:1-31:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.IPEC.2025.31

Author Details

Benjamin Bergougnoux
  • Aix-Marseille Université, CNRS, LIS, Marseille, France
Lars Jaffke
  • NHH Norwegian School of Economics, Bergen, Norway

Acknowledgements

We thank Richard Wols for the counterexample presented in Section 2.1.

References

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