{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R345",
  "content_hash": null,
  "slug": "gtc-attempt-lobster-spine",
  "type": "attempt",
  "title": "Extend the caterpillar construction to lobsters",
  "summary": "Adapt the zig-zag spine labeling to trees whose vertices lie within distance two of a path.",
  "relevance": "For Graceful tree conjecture, record gtc-attempt-lobster-spine (“Extend the caterpillar construction to lobsters”) documents a concrete method, search boundary, or failed route. The record states: Adapt the zig-zag spine labeling to trees whose vertices lie within distance two of a path.",
  "relevance_source": "recorded",
  "body": "The caterpillar proof walks the spine and takes labels alternately from the two ends of the range. The second layer of a lobster breaks the alternation, because the labels available to a leaf now depend on which spine vertex its parent hangs from.\n\nPartial results exist for restricted lobsters, so check the survey for the cases already handled before choosing a family. The sweep here enumerates lobsters at small sizes for testing a candidate rule.",
  "status": "open_strategy",
  "evidence_grade": "proposed",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://www.combinatorics.org/ojs/index.php/eljc/article/view/DS6",
      "locator": "Gallian, Dynamic Survey of Graph Labeling, lobsters"
    },
    "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, lobsters"
  },
  "models": [],
  "relations": [
    {
      "slug": "gtc-problem-lobsters",
      "title": "Bermond's lobster conjecture",
      "object_type": "problem",
      "relation": "attempts",
      "direction": "outgoing"
    },
    {
      "slug": "R348",
      "title": "Every caterpillar is graceful",
      "object_type": "claim",
      "relation": "uses",
      "direction": "outgoing"
    },
    {
      "slug": "graceful-tree-conjecture",
      "title": "graceful tree conjecture",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}