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  "path": "/abs/2602.23867v1",
  "publishedAt": "2026-03-02T01:00:00.000Z",
  "site": "https://arxiv.org",
  "tags": [
    "Karolina Drabik",
    "Maël Dumas",
    "Colin Geniet",
    "Jakub Nowakowski",
    "Michał Pilipczuk",
    "Szymon Toruńczyk"
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  "textContent": "**Authors:** Karolina Drabik, Maël Dumas, Colin Geniet, Jakub Nowakowski, Michał Pilipczuk, Szymon Toruńczyk\n\nMerge-width is a recently introduced family of graph parameters that unifies treewidth, clique-width, twin-width, and generalised colouring numbers. We prove the equivalence of several alternative definitions of merge-width, thus demonstrating the robustness of the notion. Our characterisation via definable merge-width uses vertex orderings inspired by generalised colouring numbers from sparsity theory, and enables us to obtain the first non-trivial approximation algorithm for merge-width, running in time $n^{O(1)} \\cdot 2^n$. We also obtain a new characterisation of bounded clique-width in terms of vertex orderings, and establish that graphs of bounded merge-width admit sparse quotients with bounded strong colouring numbers, are quasi-isometric to graphs of bounded expansion, and admit neighbourhood covers with constant overlap. We also discuss several other variants of merge-width and connections to adjacency labelling schemes.",
  "title": "Variants of Merge-Width and Applications"
}