{
  "abstract": "We prove that deciding whether a graph has lettericity at most k is NP-complete, even for four-colorable comparability graphs. Our reduction maps a bipartite graph G to the graph obtained from its incidence graph by inflating each vertex by a clique or an independent set of three vertices. The lettericity of this graph is determined by the numbers of vertices and edges of G and the greatest number of edge-disjoint paths on four vertices in G. Teypaz and Rapine showed that deciding whether the edges of a bipartite graph can be partitioned into paths on four vertices is NP-complete.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.06482",
  "author_total": 1,
  "authors": [
    {
      "name": "Vincent Vatter"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/90ssa8896zrtv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.06482",
  "fulltext_url": null,
  "id": "90ssa8896zrtv",
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  "landing_url": "https://arxiv.org/abs/2610.06482",
  "language": null,
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  "licence_label": "arXiv licence",
  "licence_source": "article",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
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  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.06482",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/90ssa8896zrtv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.06482",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.06482"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Deciding lettericity is NP-complete, even for four-colorable comparability graphs",
  "title_text": "Deciding lettericity is NP-complete, even for four-colorable comparability graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/90ssa8896zrtv",
  "venue": "arXiv",
  "versions": []
}