{"data":{"id":"txgraffiti-indep-domination-2020","statement_oneline":"For r-regular graphs (r at least 3), the independent domination number is at most the minimum maximal matching number.","statement_full_latex":"For every connected $r$-regular graph $G$ with $r \\ge 3$, $i(G) \\le \\mu^{*}(G)$, where $i$ is the independent domination number and $\\mu^{*}$ the minimum maximal matching (saturation) number.","source":{"title":"Machine-generated conjecture (TxGraffiti program), surveyed in 'In Reverie Together' (2025)","arxiv":"2507.17780","url":"https://arxiv.org/abs/2507.17780","year":2020,"area":"math.CO"},"renown":{"score":1,"rationale":"A specialist conjecture from automated conjecturing, open since 2020."},"attackability":{"score":4,"rationale":"Both invariants exactly computable by ILP at searchable sizes; generalized Petersen graphs sit on the equality ridge in large numbers, giving abundant seeds. A July 2026 structured search (several hundred exact evaluations plus ridge hill-climbing) found a wide equality plateau but no crossing, suggesting a hidden counting obstruction.","subscores":{"finite_witness":5,"oracle_cost":3,"freshness":3,"seedability":5}},"status":"open","last_verified_open":"2026-07-22","added":"2026-07-24","effective_status":"open","claims":[],"status_events":[{"id":"seed-txgraffiti-indep-domination-2020","conjecture_id":"txgraffiti-indep-domination-2020","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."}