erdős #593
Characterize those finite 3-uniform hypergraphs which appear in every 3-uniform hypergraph of chromatic number .
Worked, still open.
set theory · open · prize $500 · formalized (Lean) · 0 attempts
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unverified AI candidates (2)
gpt-erdos · GPT-5.2 Pro + Deep Research · unverified
Let $F$ be a **finite 3‑uniform hypergraph** (a “triple system”). Call $F$ **obligatory** (aka *unavoidable*) if **every** 3‑uniform hypergraph $H$ with (\chi(H)>\aleph_0) contains a (not necessarily induced) copy of $F$. This is exactly the notion used in the modern literature on “obligatory hypergraphs”. ([arXiv][1])
candidate solution ↗llm-hunter · gpt pro 5.2 · unverified
1 LLM attack(s) recorded (gpt pro 5.2); unverified.
candidate solution ↗formal
AMS 5 · open (literature)
theorem erdos_593 : answer(sorry) ↔
∀ (W : Type) [Fintype W] (F : ThreeUniformHypergraph W),
IsObligatory F ↔ F.IsTwoColorableformal-conjectures/593.lean ↗status
open