{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R348",
  "content_hash": null,
  "slug": "gtc-claim-caterpillars",
  "type": "claim",
  "title": "Every caterpillar is graceful",
  "summary": "Rosa's zig-zag labeling gives a graceful labeling, in fact an alpha-labeling, for every caterpillar.",
  "relevance": "For Graceful tree conjecture, record gtc-claim-caterpillars (“Every caterpillar is graceful”) records a bound, answer, status fact, or structural consequence. The record states: Rosa's zig-zag labeling gives a graceful labeling, in fact an alpha-labeling, for every caterpillar.",
  "relevance_source": "recorded",
  "body": "Walk the spine and assign labels alternately from the low end and the high end of the available range. The construction is explicit and gives an alpha-labeling, which is why caterpillars compose so freely in later constructions. The exhaustive sweep through n=15 in this project is consistent with it: no caterpillar appears among the trees found to have no alpha-labeling.",
  "status": "established",
  "evidence_grade": "sourced",
  "scope": {
    "kind": "family",
    "statement": "caterpillars, of any size",
    "family": "caterpillars"
  },
  "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, Rosa 1967"
    },
    "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, Rosa 1967"
  },
  "models": [],
  "relations": [
    {
      "slug": "graceful-tree-conjecture",
      "title": "Graceful tree conjecture",
      "object_type": "problem",
      "relation": "supports",
      "direction": "outgoing"
    },
    {
      "slug": "R345",
      "title": "Extend the caterpillar construction to lobsters",
      "object_type": "attempt",
      "relation": "uses",
      "direction": "incoming"
    },
    {
      "slug": "graceful-tree-conjecture",
      "title": "graceful tree conjecture",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}