{
  "abstract": "A $k$-arrangement of pseudolines is a set of bi-infinite curves in the plane such that any two of them intersect each other in exactly $k$ points, at which they cross, and it is simple if no three curves meet at a common point. Cyclic arrangements are the only simple $1$-arrangements of pseudolines that are unavoidable, in the Ramsey spirit: for each fixed $m\\ge 1$, every sufficiently large simple $1$-arrangement of pseudolines has a cyclic subarrangement of size $m$. We show that, for every $m\\ge 3$, the number of unavoidable simple $k$-arrangements of pseudolines of size $m$ grows exponentially with $k$, independently of $m$. For even $k$, we prove an analogous result for $k$-arrangements of pseudocircles.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.00773",
  "author_total": 3,
  "authors": [
    {
      "name": "Jan Kynčl"
    },
    {
      "name": "Carolina Medina"
    },
    {
      "name": "Gelasio Salazar"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bkng3k5n335qd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.00773",
  "fulltext_url": null,
  "id": "bkng3k5n335qd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.00773",
  "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",
      "cs.CG"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2607|Limits and Structures in Graph Theory"
    ]
  ],
  "openalex": "W7216461335",
  "pdf_url": "https://arxiv.org/pdf/2610.00773",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bkng3k5n335qd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.00773",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.00773"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "$k$-arrangements of pseudolines and pseudocircles",
  "title_text": "k-arrangements of pseudolines and pseudocircles",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/bkng3k5n335qd",
  "venue": "arXiv",
  "versions": []
}