{"data":{"id":"vizing-1968","statement_oneline":"Domination numbers satisfy γ(G□H) ≥ γ(G)γ(H) for the Cartesian product of any two graphs.","statement_full_latex":"For all graphs $G$ and $H$, $\\gamma(G \\square H) \\ge \\gamma(G)\\,\\gamma(H)$, where $\\gamma$ denotes the domination number and $\\square$ the Cartesian product.","source":{"title":"Some unsolved problems in graph theory (Vizing)","arxiv":null,"url":"https://en.wikipedia.org/wiki/Vizing%27s_conjecture","year":1968,"area":"math.CO"},"renown":{"score":5,"rationale":"The central open problem of domination theory for six decades; active work as recently as July 2026 (constant-factor improvements by Steiner and by Aliabadi-Krop)."},"attackability":{"score":2,"rationale":"Finite witness (a pair of graphs) with an ILP oracle, but decades of minimal-counterexample theorems (no chordal or claw-free factors, factor domination numbers at least 4) fence the search into a hard region.","subscores":{"finite_witness":5,"oracle_cost":3,"freshness":1,"seedability":3}},"status":"open","last_verified_open":"2026-07-23","added":"2026-07-24","effective_status":"open","claims":[],"status_events":[{"id":"seed-vizing-1968","conjecture_id":"vizing-1968","status":"open","date":"2026-07-24T00:00:00.000Z","note":"Loaded from seed data."}],"resolutions":[]},"notice":"Status is community- and machine-tracked and may lag. Verify independently before investing effort."}