Written on the Wall IICombinatorics
Written on the Wall II - Conjecture 316
WOWII Conjecture 316
Mathematical statement
WOWII Conjecture 316
Let G be a simple connected graph and let P denote the set of pendant vertices
(vertices of degree 1). If |P| ≥ deg_avg(Gᶜ), then G is well totally dominated,
where deg_avg(Gᶜ) is the average degree of the complement of G.
Statement source: Written on the Wall II 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
conjecture316
theorem conjecture316 (G : SimpleGraph α) [DecidableRel G.Adj] (hG : G.Connected) (h : (averageDegree Gᶜ : ℚ) ≤ (pendantVertices G).card) : IsWellTotallyDominated G := 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