{
  "abstract": "A king in a tournament is a vertex from which every other vertex is reachable by a directed path of length at most two. We study the deterministic query complexity of finding a king when a query specifies a set of vertices and returns the number of edges directed from that set to its complement. We prove that this complexity is $Θ(n)$ for $n$-vertex tournaments. To show this, we first show that every correct deterministic algorithm in this model must output a maximum-outdegree vertex, even though a king need not have maximum outdegree. We then give an adversary whose answers, after too few queries, remain consistent with a tournament in which the algorithm's output does not have maximum outdegree.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.40521",
  "author_total": 3,
  "authors": [
    {
      "name": "Ziad Ismaili Alaoui"
    },
    {
      "name": "Oded Lachish"
    },
    {
      "name": "Nikhil S. Mande"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2z6yv0knjjfm6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.40521",
  "fulltext_url": null,
  "id": "2z6yv0knjjfm6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.40521",
  "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",
      "cs.CC"
    ],
    [
      "arxiv",
      "math.CO"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.40521",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2z6yv0knjjfm6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:35Z",
      "native_id": "2610.40521",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.40521"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Directed Cut-Query Complexity of Finding a King",
  "title_text": "Directed Cut-Query Complexity of Finding a King",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:53Z",
  "url": "https://research.draconitic.com/paper/2z6yv0knjjfm6",
  "venue": "arXiv",
  "versions": []
}