{
  "abstract": "Let $f(k)$ denote the smallest integer such that every oriented graph $D$ with chromatic number at least $f(k)$ contains every oriented tree on $k$ vertices. Burr (1980) showed that $f(k)\\le (k-1)^2$ and conjectured that $f(k)=2k-2$. Bessy, Gonçalves and Reinald (2025) proved that $f(k)=O(k^{3/2})$. In this paper, by using an absorbing set method, we show that $f(k)\\le \\lfloor 31\\log (k!)\\rfloor=O(k\\log k)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.18175",
  "author_total": 3,
  "authors": [
    {
      "name": "Liangdong Fan"
    },
    {
      "name": "Junying Lu"
    },
    {
      "name": "Yaojun Chen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/db2e66ck2g4b2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.18175",
  "fulltext_url": null,
  "id": "db2e66ck2g4b2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.18175",
  "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",
      "math.CO"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.18175",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/db2e66ck2g4b2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:04Z",
      "native_id": "2609.18175",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.18175"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A near-linear upper bound for Burr's conjecture",
  "title_text": "A near-linear upper bound for Burr's conjecture",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:04Z",
  "url": "https://research.draconitic.com/paper/db2e66ck2g4b2",
  "venue": "arXiv",
  "versions": []
}