Erdős Problem 593: Obligatory Implies Two Colorable
Erdős Problem 593 , Necessary direction*: Every obligatory finite 3-uniform hypergraph is 2-colorable.
Mathematical statement
Erdős Problem 593 , Necessary direction*: Every obligatory finite 3-uniform hypergraph is 2-colorable.
This is the natural necessary condition for the conjectural characterization in erdos_593:
if a finite 3-uniform hypergraph F is not 2-colorable, one expects to construct a
hypergraph with large chromatic number that contains no copy of F.
Statement source: Erdős Problems statement material
Statement terms: Source-specific
Source-specific terms. Therefore does not assert reuse rights beyond attributed display.
Statement artifacts, not proofs
These records expose exact Lean propositions and statement-only wrappers. Defining a proposition does not supply a proof of it. A placeholder-bearing target also contains no proof. Elaboration checks syntax and types; it does not certify that a formalization perfectly captures every nuance of the informal problem.
Pinned Lean formulation 1
erdos_593.variants.obligatory_implies_two_colorable
theorem erdos_593.variants.obligatory_implies_two_colorable : answer(sorry) ↔ ∀ (W : Type) [Fintype W] (F : ThreeUniformHypergraph W), IsObligatory F → F.IsTwoColorable := by sorry- Statement source
- Formal Conjectures
- Lean version
- v4.27.0
- Placeholder
- Present; no proof artifact
- Source evidence
- Pinned source index
- Fidelity review
- Community formulation
References