{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R350",
  "content_hash": null,
  "slug": "gtc-claim-diameter-five",
  "type": "claim",
  "title": "Trees of diameter at most five are graceful",
  "summary": "The diameter ladder is settled through five, by Hrncar and Haviar for the diameter-five case.",
  "relevance": "For Graceful tree conjecture, record gtc-claim-diameter-five (“Trees of diameter at most five are graceful”) records a bound, answer, status fact, or structural consequence. The record states: The diameter ladder is settled through five, by Hrncar and Haviar for the diameter-five case.",
  "relevance_source": "recorded",
  "body": "Diameters up to four follow from earlier constructions; diameter five is the substantial case. The proof is a construction by cases on the shape of the central path. It stops where the cases stop, which is why diameter six has needed separate work.",
  "status": "established",
  "evidence_grade": "sourced",
  "scope": {
    "kind": "family",
    "statement": "trees of diameter at most five, of any size",
    "family": "diameter at most five"
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://www.combinatorics.org/ojs/index.php/eljc/article/view/DS6",
      "locator": "Gallian, Dynamic Survey of Graph Labeling, Hrncar and Haviar 2001"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://www.combinatorics.org/ojs/index.php/eljc/article/view/DS6",
    "locator": "Gallian, Dynamic Survey of Graph Labeling, Hrncar and Haviar 2001"
  },
  "models": [],
  "relations": [
    {
      "slug": "graceful-tree-conjecture",
      "title": "Graceful tree conjecture",
      "object_type": "problem",
      "relation": "supports",
      "direction": "outgoing"
    },
    {
      "slug": "R343",
      "title": "Push the diameter ladder from five to six",
      "object_type": "attempt",
      "relation": "uses",
      "direction": "incoming"
    },
    {
      "slug": "graceful-tree-conjecture",
      "title": "graceful tree conjecture",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}