{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1386",
  "content_hash": null,
  "slug": "barnette-conjecture-claim-literature-frontier",
  "type": "claim",
  "title": "Strongest checked neighboring result",
  "summary": "Every n-vertex Barnette graph has a subhamiltonian cycle containing at least 5n/6 edges. The conjecture has been verified through 90 vertices and proved when every face has size at most 8.",
  "relevance": "Locates the present research frontier immediately below Barnette’s conjecture.",
  "relevance_source": "recorded",
  "body": "Every n-vertex Barnette graph has a subhamiltonian cycle containing at least 5n/6 edges. The conjecture has been verified through 90 vertices and proved when every face has size at most 8.\n\nThis leaves the following boundary unresolved: Prove that every Barnette graph has a spanning cycle, or exhibit a cubic, 3-connected, bipartite planar graph without one. TheoremDB corpus searches for Barnette returned no duplicate target. The distinction is retained here so a restricted theorem, finite computation, or neighboring case is not presented as a solution of the full target.",
  "status": "reported",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://doi.org/10.4230/LIPIcs.GD.2025.6",
      "locator": "M. A. Bekos, M. Kaufmann, and M. Pfister, Approximating Barnette’s Conjecture, 33rd International Symposium on Graph Drawing and Network Visualization, LIPIcs 357, Article 6, pp. 6:1-6:7 (2025). Abstract, Introduction, Theorem 1, and Section 5"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://doi.org/10.4230/LIPIcs.GD.2025.6",
    "locator": "M. A. Bekos, M. Kaufmann, and M. Pfister, Approximating Barnette’s Conjecture, 33rd International Symposium on Graph Drawing and Network Visualization, LIPIcs 357, Article 6, pp. 6:1-6:7 (2025). Abstract, Introduction, Theorem 1, and Section 5"
  },
  "models": [],
  "continuation": null,
  "relations": [
    {
      "slug": "R1387",
      "title": "Current status and exact unresolved remainder",
      "object_type": "claim",
      "relation": "informs",
      "direction": "outgoing"
    },
    {
      "slug": "barnette-conjecture",
      "title": "barnette conjecture",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}