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Oriented graph two-hop reach benchmark
Family 173: Seymour’s second-neighborhood conjecture. First application triage, 9 October 2026 Australia/Brisbane.
Problem and potential new use
Graph analytics teams can compute a vertex whose exact-distance-two neighborhood is at least its one-hop neighborhood.
Applicability and commercial boundary
Excluding reciprocal edge pairs matters. The theorem is not a viral growth or influence guarantee; reach counts differ from weighted propagation.
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
Implement the simple finite check only if a graph application needs this exact property.
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.