{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R434",
  "content_hash": null,
  "slug": "ksd6-attempt-literature-search",
  "type": "attempt",
  "title": "Targeted knight-domination literature search",
  "summary": "The search found work on square covers, efficient domination, and perfect domination, with no exact ordinary three-row formula located.",
  "relevance": "For A period-six recurrence for domination on the three-row knight graph, record ksd6-attempt-literature-search (“Targeted knight-domination literature search”) documents a concrete method, search boundary, or failed route. The record states: The search found work on square covers, efficient domination, and perfect domination, with no exact ordinary three-row formula located.",
  "relevance_source": "recorded",
  "body": "Searches for ordinary domination on a three-row rectangular knight graph, knight-cover strips, and \\(KN_{n,3}\\) did not locate this six-column formula.\n\nDavid C. Fisher's 2003 paper studies the ordinary knight-cover problem on square \\(n\\times n\\) boards. Todd Fenstermacher, Soumendra Ganguly, and Renu Laskar study perfect domination on rectangular knight graphs. They define the same underlying graph \\(KN_{n,m}\\), but perfect domination requires every unselected vertex to have exactly one selected neighbor. Their three-row results consequently concern a different invariant and exhibit width classes modulo 8. That paper also points to Sinko and Slater's work on efficient domination, another stricter variant.\n\nThis search gives useful context and leaves publication novelty unresolved. The exact ordinary-domination recurrence in this entry rests on the independent finite-state proof.",
  "status": "completed",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://arxiv.org/abs/1805.03335",
      "locator": "Todd Fenstermacher, Soumendra Ganguly, and Renu Laskar, Perfect Domination in Knights Graphs, arXiv:1805.03335, Definition 1.3 and Propositions 2.3 and 3.2; David C. Fisher, On the n x n Knight Cover Problem, Ars Combinatoria 69 (2003), 255-274"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://arxiv.org/abs/1805.03335",
    "locator": "Todd Fenstermacher, Soumendra Ganguly, and Renu Laskar, Perfect Domination in Knights Graphs, arXiv:1805.03335, Definition 1.3 and Propositions 2.3 and 3.2; David C. Fisher, On the n x n Knight Cover Problem, Ars Combinatoria 69 (2003), 255-274"
  },
  "relations": [
    {
      "slug": "R435",
      "title": "The period-six recurrence holds from n=9",
      "object_type": "claim",
      "relation": "informs",
      "direction": "outgoing"
    },
    {
      "slug": "knight-strip-domination-period-six",
      "title": "knight strip domination period six",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}