{
  "abstract": "For a graph $H$, the $H$-freeness edge-deletion problem is the algorithmic problem of finding, for an input graph $G$, the minimum number of edges of $G$ whose deletion turns $G$ into an $H$-free graph. We show that for every graph $H$ containing a cycle, this problem is NP-hard. This proves a conjecture of Gishboliner, Levanzov and Shapira, and completes the characterization of the complexity of the $H$-freeness edge-deletion problem, answering a question of Alon, Shapira and Sudakov.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.09715",
  "author_total": 2,
  "authors": [
    {
      "name": "Lior Gishboliner"
    },
    {
      "name": "Ethan Honest"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a7qbw4cpkfz1a.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.09715",
  "fulltext_url": null,
  "id": "a7qbw4cpkfz1a",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.09715",
  "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.CC"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "1703|Advanced Graph Theory Research"
    ]
  ],
  "openalex": "W7212188791",
  "pdf_url": "https://arxiv.org/pdf/2609.09715",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a7qbw4cpkfz1a.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:15Z",
      "native_id": "2609.09715",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.09715"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "NP-Hardness of the $H$-Free Edge-Deletion Problem",
  "title_text": "NP-Hardness of the H-Free Edge-Deletion Problem",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:15Z",
  "url": "https://research.draconitic.com/paper/a7qbw4cpkfz1a",
  "venue": "arXiv",
  "versions": []
}