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Cycle–clique Ramsey exact reference library
Family 189: Cycle–clique Ramsey numbers. First application triage, 9 October 2026 Australia/Brisbane.
Problem and potential new use
Graph researchers can use exact small-parameter forcing formulas to validate Ramsey search examples.
Applicability and commercial boundary
Complete red-blue graphs and the specific cycle/clique objective do not imply a practical business scheduling algorithm.
Initial business decision
Research or conditional engineering only until an effective implementation and a recurring buyer problem are identified. No commercial demand or profitability is established. Where a direct product bridge is weak, the legitimate use is a research reference or evidence adapter, rather than a new standalone company.
Next verification action
Create exact small fixtures and document the exceptional triangle case.
Evidence scope
The catalog statement was individually reviewed. The manuscript proof and selected formal statement have not yet been compared in depth for this family. No independent proof verification was run. Pinned source revision fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb. See source metadata.