{
  "abstract": "An annotated graph is a pair $(G,S)$, where $G$ is a graph and $S$ is a subset of vertices of $G$. We present a unified approach for definitions of annotated versions of classical graph parameters such as treewidth, pathwidth, treedepth, etc. A generic way to incorporate a distinguished set of vertices into a graph parameter is via torsos. Given a graph $G$ and a subset $S'\\subseteq V(G)$, we define $\\mathrm{torso}_G(S')$ to be the graph with vertex set $S'$ in which distinct vertices $u,v\\in S'$ are adjacent if and only if there exists a $u$-$v$ path in $G$ whose internal vertices lie outside $S'$. Now let $\\mathrm{p}$ be any graph parameter. For an annotated graph $(G,S)$, we define the torso $\\mathrm{p}$ of $(G,S)$ by \\[\\mathrm{p}(G,S) = \\min\\{\\mathrm{p}(\\mathrm{torso}_G(S')) \\mid S \\subset S' \\subset V(G)\\}.\\] For a minor-closed class of annotated graphs $\\mathcal{C}$, we discuss equivalent conditions for $\\mathrm{p}(G,S)$ bounded for all $(G,S)\\in\\mathcal{C}$ in terms of annotated graphs excluded in $\\mathcal{C}$. In many cases, we collect known results from the literature. We include two new arguments for $\\mathrm{p}$ being the $2$-treedepth and the feedback vertex number. Among other statements, we also include a variant of the Erdős-Pósa property for annotated cycles. We propose some new research directions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.25905",
  "author_total": 6,
  "authors": [
    {
      "name": "Maël Dumas"
    },
    {
      "name": "Jędrzej Hodor"
    },
    {
      "name": "Tomasz Mazur"
    },
    {
      "name": "Piotr Micek"
    },
    {
      "name": "Clément Rambaud"
    },
    {
      "name": "Giannos Stamoulis"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6qvq0053v13xt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.25905",
  "fulltext_url": null,
  "id": "6qvq0053v13xt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.25905",
  "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": "W7223052574",
  "pdf_url": "https://arxiv.org/pdf/2610.25905",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6qvq0053v13xt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.25905",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.25905"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Invitation to torso parameters of annotated graphs",
  "title_text": "Invitation to torso parameters of annotated graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/6qvq0053v13xt",
  "venue": "arXiv",
  "versions": []
}