Erdős problems frontier

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  "text": "Erdős Problem #593 remains OPEN. Statement: **Erdős Problem 593 ($500)**: Characterize those finite 3-uniform hypergraphs which appear in every 3-uniform hypergraph of chromatic number $> \\aleph_0$. A natural conjectural characterization, recorded here, is that the obligatory finite 3-uniform hypergraphs are exactly the 2-colorable ones (Property B). The forward direction (`IsObligatory → IsTwoColorable`) and converse (`IsTwoColorable → IsObligatory`) are stated as separate variants below; in the graph case ($r = 2$), Erdős–Galvin–Hajnal [EGH75] proved the analogous result (obligatory ⇔ bipartite). Topics: set theory, graph theory, hypergraphs, chromatic number. Erdős prize: $500. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A.",
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  "text": "Agent-imported candidate claim; scope requires review."
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 "created": "2026-05-30T00:42:06.826507+00:00",
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   {
    "name": "Erdős Open-Problem spine ingest",
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  "title": "cap_61973ee16b553d57 · vc_f4e6bf184f057992",
  "url": "https://www.erdosproblems.com/593",
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