{
  "abstract": "A set S of vertices of a graph is odd independent if it is independent and every vertex outside S has either zero or an odd number of neighbors in S. The largest size of such a set is the odd independence number alpha_od. Caro, Petrusevski, Skrekovski and Tuza [2] conjectured that alpha_od = 1 for every finite Queen graph. They also asked whether the infinite Queen graph has alpha_od = 1 or alpha_od = infinity. We prove that alpha_od = 1 in both cases. In particular, in the case of an infinite board we prove that alpha_od = 1 holds on the quarter plane and on the whole plane.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.19024",
  "author_total": 3,
  "authors": [
    {
      "name": "Martin Knor"
    },
    {
      "name": "Jelena Sedlar"
    },
    {
      "name": "Riste Škrekovski"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e0jvvscmhyazc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.19024",
  "fulltext_url": null,
  "id": "e0jvvscmhyazc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.19024",
  "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",
      "1703|Advanced Graph Theory Research"
    ]
  ],
  "openalex": "W7203931825",
  "pdf_url": "https://arxiv.org/pdf/2608.19024",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e0jvvscmhyazc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2608.19024",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.19024"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "On the odd independence number of the Queen graph",
  "title_text": "On the odd independence number of the Queen graph",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/e0jvvscmhyazc",
  "venue": "arXiv",
  "versions": []
}