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

Benjamin Bergougnoux; Lars Jaffke

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arXiv · 2507.00612

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

Benjamin Bergougnoux·Lars Jaffke

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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, Lars Jaffke. 2025-07-01. Hamiltonicity Parameterized by Mim-Width is (Indeed) Para-NP-Hard. https://arxiv.org/abs/2507.00612

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