Erdős Problem #902
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
`HasPropertyS G n` is Schütte's property \(S_n\) [Er63c]: every set `E` of `n` vertices is dominated by a vertex outside it, that is, some vertex `x ∉ E` has an edge to every vertex of `E`.
\(f(n)\): the least number of vertices of a tournament with property \(S_n\). A tournament with fewer than \(n\) vertices has no set of \(n\) vertices, so it has property \(S_n\) vacuously; the condition `n ≤ m` excludes this case.
Attempts
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Verified \(48\leq f(4)\leq67\); \(P_{67}\) is an explicit \(S_4\) tournament with a standalone exhaustive checker, while the asymptotic factor-\(n\) gap remains open.
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