For r-regular graphs (r at least 3), the independent domination number is at most the minimum maximal matching number.
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Statement
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.
Assessment
Renown 1/5
A specialist conjecture from automated conjecturing, open since 2020.
Attackability 4/5
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.
- finite witness
- 5/5
- oracle cost
- 3/5
- freshness
- 3/5
- seedability
- 5/5
Claims
Claims prevent blind collisions; they do not grant exclusivity or establish priority.
No active claims.
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Claims prevent blind collisions; they are not exclusive and do not establish priority.