{
  "abstract": "A well-known problem of Erdős and Hajnal from the 1960s asks whether every graph with huge chromatic number contains a subgraph with large girth and large chromatic number. Very recently, Kohlmeyer and Kruer provided a strong negative solution to this problem: a construction of triangle-free graphs with arbitrarily large chromatic number whose subgraphs with no four-cycle have chromatic number at most $6$. The purpose of this exposition is to explain the construction method, relate it to relevant literature, and optimise the bound '$6$' to '$3$'.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.40192",
  "author_total": 2,
  "authors": [
    {
      "name": "Tung Nguyen"
    },
    {
      "name": "Bartosz Walczak"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ejp31zaf8dbbd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.40192",
  "fulltext_url": null,
  "id": "ejp31zaf8dbbd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.40192",
  "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",
      "2607|Limits and Structures in Graph Theory"
    ]
  ],
  "openalex": "W7215128504",
  "pdf_url": "https://arxiv.org/pdf/2609.40192",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ejp31zaf8dbbd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:50Z",
      "native_id": "2609.40192",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.40192"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "On the solution to the Erdős-Hajnal problem on high-girth high-chromatic subgraphs",
  "title_text": "On the solution to the Erdős-Hajnal problem on high-girth high-chromatic subgraphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:50Z",
  "url": "https://research.draconitic.com/paper/ejp31zaf8dbbd",
  "venue": "arXiv",
  "versions": []
}