{
  "abstract": "A $k$-quasiplanar graph is a graph drawn in the plane with no $k$ pairwise crossing edges. Pach, Shahrokhi, and Szegedy conjectured that every such graph on $n$ vertices has $O_k(n)$ edges. ChatGPT produced a proof of this conjecture. Here, we present a simplified, self-contained version of that proof.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.07314",
  "author_total": 3,
  "authors": [
    {
      "name": "János Pach"
    },
    {
      "name": "Gábor Tardos"
    },
    {
      "name": "Ji Zeng"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/172rdmqg2f9pj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.07314",
  "fulltext_url": null,
  "id": "172rdmqg2f9pj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.07314",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.07314",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/172rdmqg2f9pj.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:34Z",
      "native_id": "2611.07314",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.07314"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "On the number of edges in quasiplanar graphs",
  "title_text": "On the number of edges in quasiplanar graphs",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:47Z",
  "url": "https://research.draconitic.com/paper/172rdmqg2f9pj",
  "venue": "arXiv",
  "versions": []
}