{
  "abstract": "The Nash-Williams--Tutte theorem characterizes the existence of $k$ edge-disjoint spanning trees by a condition on every vertex partition. We prove that, for simple graphs, the same condition guarantees $k$ edge-disjoint spanning trees, each of diameter $O(n/δ)$ and with $O((n/δ)\\log(δ+1))$ internal vertices, where $n$ is the number of vertices and $δ$ is the minimum degree. Both bounds hold simultaneously for every tree, with absolute implicit constants independent of $k$, and each is asymptotically optimal in general. Our proof is constructive and yields a randomized algorithm with expected running time $\\tilde{O}(n^5)$. We derive applications to short edge-disjoint routes and weak linkages, small Steiner trees, and survivable networks with short paths. The joint bounds also yield low-diameter spanning Eulerian subgraphs and short tours for postman and general routing problems.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.05043",
  "author_total": 4,
  "authors": [
    {
      "name": "Pin-Hsian Lee"
    },
    {
      "name": "Peng-Ting Lin"
    },
    {
      "name": "Meng-Tsung Tsai"
    },
    {
      "name": "Ting-An Wu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a4cd4e8v5c8ph.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.05043",
  "fulltext_url": null,
  "id": "a4cd4e8v5c8ph",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.05043",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.DM"
    ],
    [
      "arxiv",
      "cs.DS"
    ],
    [
      "arxiv",
      "math.CO"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.05043",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a4cd4e8v5c8ph.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:29Z",
      "native_id": "2611.05043",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.05043"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A Low-Diameter Nash-Williams--Tutte Theorem",
  "title_text": "A Low-Diameter Nash-Williams--Tutte Theorem",
  "type": "preprint",
  "updated_at": "2026-11-04T15:21:29Z",
  "url": "https://research.draconitic.com/paper/a4cd4e8v5c8ph",
  "venue": "arXiv",
  "versions": []
}