{
  "abstract": "In the localization game on a graph $G$, a team of cops searches for an invisible, mobile robber on $G$ by \"probing\" vertices; each probe tells the cops the distance from the probed vertex to the robber. The cops win if they can uniquely determine the robber's location. In this paper, we introduce a related game: the directional localization game. In this game, instead of probes returning distances, they return directions: when the cops probe a vertex $v$, the robber must respond with one or more neighbors of $v$ that lie on a shortest path from $v$ to the robber's location. The minimum number of cops needed to win this game on $G$ is the directional localization number of $G$. We study the directional localization game on several classes of graphs, including chordal graphs, Cartesian products, and incidence graphs of projective planes. We also bound the directional localization number of a graph $G$ in terms of the degeneracy and the treewidth of $G$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.01745",
  "author_total": 2,
  "authors": [
    {
      "name": "John Jones"
    },
    {
      "name": "William B. Kinnersley"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/14z0ghg475pws.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.01745",
  "fulltext_url": null,
  "id": "14z0ghg475pws",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.01745",
  "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",
      "math.CO"
    ],
    [
      "openalex",
      "1703|Advanced Graph Theory Research"
    ]
  ],
  "openalex": "W7207550749",
  "pdf_url": "https://arxiv.org/pdf/2609.01745",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/14z0ghg475pws.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:20Z",
      "native_id": "2609.01745",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.01745"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "The directional localization game on graphs",
  "title_text": "The directional localization game on graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:20Z",
  "url": "https://research.draconitic.com/paper/14z0ghg475pws",
  "venue": "arXiv",
  "versions": []
}