{
  "abstract": "We characterize the uniform computational strength of finding one-way Eulerian paths in countable graphs. For both directed and undirected graphs, this problem is Weihrauch-equivalent to $\\mathsf{lim}\\times\\mathsf{C}_{\\mathbb{N}}'$, where $\\mathsf{C}_{\\mathbb{N}}'$ is the jump of closed choice on the natural numbers. This refines the proof-theoretical strength of the existence of an Eulerian path given by the reverse mathematics framework. The $\\mathsf{C}_{\\mathbb{N}}'$ component comes entirely from the difficulty of choosing a starting vertex: with a valid start prescribed, the problem is equivalent to $\\mathsf{lim}$. We also study the problem $\\mathsf{OrientEP}$ of orienting an undirected graph while preserving the existence of a one-way Eulerian path. We prove $\\mathsf{lim}_2<_{\\mathrm{W}}\\mathsf{OrientEP}<_{\\mathrm{W}}\\mathsf{C}_{2}'\\sqcap\\mathsf{Sort}_2$ and $\\mathsf{OrientEP}\\not\\le_{\\mathrm{W}}\\mathsf{C}_{\\mathbb{N}}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.00818",
  "author_total": 1,
  "authors": [
    {
      "name": "Manlio Valenti"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2mtpgxe8sd073.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.00818",
  "fulltext_url": null,
  "id": "2mtpgxe8sd073",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.00818",
  "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",
      "math.CO"
    ],
    [
      "arxiv",
      "math.LO"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.00818",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2mtpgxe8sd073.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.00818",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.00818"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "Well begun is half done: the computation of Eulerian paths",
  "title_text": "Well begun is half done: the computation of Eulerian paths",
  "type": "preprint",
  "updated_at": "2026-11-03T12:21:10Z",
  "url": "https://research.draconitic.com/paper/2mtpgxe8sd073",
  "venue": "arXiv",
  "versions": []
}