Erdős Problem 593: Two Colorable Implies Obligatory
Erdős Problem 593 , Sufficient direction*: Every finite 2-colorable 3-uniform hypergraph is obligatory.
Mathematical statement
Erdős Problem 593 , Sufficient direction*: Every finite 2-colorable 3-uniform hypergraph is obligatory.
This is the converse direction of the erdos_593 characterization: if 2-colorability
matches the graph-case characterization (bipartite ⇔ obligatory), then every 2-colorable
finite 3-uniform hypergraph must appear in every 3-uniform hypergraph of chromatic number
.
Together with erdos_593.variants.obligatory_implies_two_colorable, this implies erdos_593.
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.two_colorable_implies_obligatory
theorem erdos_593.variants.two_colorable_implies_obligatory : answer(sorry) ↔ ∀ (W : Type) [Fintype W] (F : ThreeUniformHypergraph W), F.IsTwoColorable → IsObligatory F := 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