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arXiv · 2504.08266

$χ$-Boundedness and Neighbourhood Complexity of Bounded Merge-Width Graphs

Marthe Bonamy·Colin Geniet
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Abstract

Merge-width, recently introduced by Dreier and Toruńczyk, is a common generalisation of bounded expansion classes and twin-width for which the first-order model checking problem remains tractable. We prove that a number of basic properties shared by bounded expansion and bounded twin-width graphs also hold for bounded merge-width graphs: they are $χ$-bounded, they satisfy the strong Erdős-Hajnal property, and their neighbourhood complexity is linear.

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Marthe Bonamy, Colin Geniet. 2025-06-16. $χ$-Boundedness and Neighbourhood Complexity of Bounded Merge-Width Graphs. https://arxiv.org/abs/2504.08266

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