{"data":{"id":"graceful-tree-1967","statement_oneline":"Every tree admits a graceful labeling.","statement_full_latex":"Every tree on $n$ vertices has a labeling by $\\{0,\\dots,n-1\\}$ whose edge labels $|f(u)-f(v)|$ are exactly $\\{1,\\dots,n-1\\}$ (Ringel-Kotzig).","source":{"title":"Graceful tree conjecture (Ringel-Kotzig 1967)","arxiv":null,"url":"https://en.wikipedia.org/wiki/Graceful_labeling","year":1967,"area":"math.CO"},"renown":{"score":3,"rationale":"The best-known conjecture in graph labeling; the related Ringel conjecture was proved in 2020.","scored_by":"founder"},"attackability":{"score":2,"rationale":"A counterexample is a single tree failing an exhaustive labeling search -- checkable but expensive; all trees through ~35 vertices are verified graceful, and probabilistic results cover large trees.","subscores":{"finite_witness":5,"oracle_cost":2,"freshness":1,"seedability":1},"scored_by":"founder"},"status":"open","last_verified_open":"2026-01-15","added":"2026-07-25","ranking_score":6,"verification_tier":null,"ai_systems":[],"posed_by":null,"years_open":null,"notability":null,"source_trackers":[],"resolution_type":null,"resolver":null,"resolution_date":null,"evidence_url":null,"evidence_note":null,"method_note":null,"effective_status":"open","claims":[],"status_events":[{"id":"seed-graceful-tree-1967","conjecture_id":"graceful-tree-1967","status":"open","date":"2026-07-25T00:00:00.000Z","actor":"human-admin","rationale":"Loaded from unified seed data.","note":"Loaded from unified seed data."}],"public_actions":[{"name":"claim","method":"POST","href":"/c/graceful-tree-1967/claim","verification":"email magic link"},{"name":"report_resolution","method":"POST","href":"/c/graceful-tree-1967/resolve","verification":"admin review"}],"resolutions":[]},"notice":"Status is community- and machine-tracked and may lag. Verify independently before investing effort."}