{
  "abstract": "For a graph $H$, $\\langle H \\rangle$ denotes the class of all subdivisions of $H$ and $tw(H)$ denotes the treewidth of $H$. In this paper, we prove the following. For $k\\geq 1, R\\geq 1$, let $G,H$ be two graphs such that strong isometric path complexities (Chakraborty et al. [\\textsc{Disc. Math., 2026}]) of both $G$ and $\\langle H \\rangle$ are at most $k$, and $G$ admits an honest, ``nicely rooted'' $R$-bounded $H$-partition. Then, there is a graph $F$ with $tw(F)\\leq tw(H)$ such that $G$ admits a $(1,33\\cdot R\\cdot k^2)$-quasi-isometry to $F$. Using results of Albrechtsen, Distel, and Georgakopoulos (2025), we also obtain that $K_{2,t}$-asymptotic minor-free graphs admit quasi-isometries with additive distortion to $K_{2,t}$-minor-free graphs. This answers an open question raised by the above authors. As part of our proof, we combine the graph-partition based method and the layering partition based method (Chepoi et al. [\\textsc{Discrete Comput. Geom.} 2012]) to obtain additive quasi-isometry when both the source and all subdivisions of the target graph have bounded strong isometric path complexity.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.36186",
  "author_total": 2,
  "authors": [
    {
      "name": "Dibyayan Chakraborty"
    },
    {
      "name": "Yann Vaxès"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0f436gedqv9gn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.36186",
  "fulltext_url": null,
  "id": "0f436gedqv9gn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.36186",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.DM"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "1703|Advanced Graph Theory Research"
    ]
  ],
  "openalex": "W7214948628",
  "pdf_url": "https://arxiv.org/pdf/2609.36186",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0f436gedqv9gn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.36186",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.36186"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Additive Quasi-isometry via rooted graph partitions and layering partition",
  "title_text": "Additive Quasi-isometry via rooted graph partitions and layering partition",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/0f436gedqv9gn",
  "venue": "arXiv",
  "versions": []
}