{"data":{"id":"tuza-1981","statement_oneline":"The minimum number of edges meeting all triangles is at most twice the maximum number of edge-disjoint triangles.","statement_full_latex":"For every graph $G$, $\\tau_{\\triangle}(G) \\le 2\\,\\nu_{\\triangle}(G)$: the triangle edge-cover number is at most twice the triangle packing number.","source":{"title":"Tuza's conjecture (1981)","arxiv":null,"url":"https://en.wikipedia.org/wiki/Tuza%27s_conjecture","year":1981,"area":"math.CO"},"renown":{"score":3,"rationale":"A benchmark problem in extremal combinatorics; the constant 2 is tight for K4 and K5.","scored_by":"founder"},"attackability":{"score":2,"rationale":"Finite witness with LP/ILP oracles; fractional version proved (Krivelevich), 2.87 bound known, tight examples (K4, K5) are natural seeds but decades of attention have found no violation.","subscores":{"finite_witness":5,"oracle_cost":3,"freshness":1,"seedability":3},"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-tuza-1981","conjecture_id":"tuza-1981","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/tuza-1981/claim","verification":"email magic link"},{"name":"report_resolution","method":"POST","href":"/c/tuza-1981/resolve","verification":"admin review"}],"resolutions":[]},"notice":"Status is community- and machine-tracked and may lag. Verify independently before investing effort."}