{
  "abstract": "The oriented diameter of a connected bridgeless graph is the minimum diameter of a strong orientation. Let $f(d)$ be the maximum oriented diameter among all such graphs of diameter $d$. In 1978, Chvátal and Thomassen proved $f(d)\\le2d^2+2d$ and constructed graphs showing that any quadratic upper bound on $f(d)$ must have leading coefficient at least $1/2$. We prove that $f(d)\\le \\tfrac12d^2+7d$ for every integer $d\\ge1$. This matches the leading coefficient of their lower bound and establishes $f(d)=\\tfrac12d^2+O(d)$, determining the optimal quadratic coefficient. Our proof gives a polynomial-time algorithm that constructs a strong orientation satisfying the stated bound.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.04660",
  "author_total": 4,
  "authors": [
    {
      "name": "Jiangdong Ai"
    },
    {
      "name": "Yaokun Feng"
    },
    {
      "name": "Hui Lei"
    },
    {
      "name": "Zijian Ren"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4ct4dqqze60gb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.04660",
  "fulltext_url": null,
  "id": "4ct4dqqze60gb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.04660",
  "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"
    ],
    [
      "openalex",
      "1703|Advanced Graph Theory Research"
    ]
  ],
  "openalex": "W7220739001",
  "pdf_url": "https://arxiv.org/pdf/2610.04660",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4ct4dqqze60gb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.04660",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.04660"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "The asymptotic maximum oriented diameter of graphs",
  "title_text": "The asymptotic maximum oriented diameter of graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/4ct4dqqze60gb",
  "venue": "arXiv",
  "versions": []
}