Written on the Wall IICombinatorics
Written on the Wall II - Conjecture 322
WOWII Conjecture 322
Mathematical statement
WOWII Conjecture 322
Let G be a simple connected graph on n ≥ 5 vertices. If the maximum over all
vertices v of l(v) , the independence number of the neighborhood N(v) of v
, is at most 1, then G is well totally dominated.
Here l(v) = α(G[N(v)]) is the independence number of the subgraph induced by the
open neighborhood of v.
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
conjecture322
theorem conjecture322 (G : SimpleGraph α) [DecidableRel G.Adj] (hG : G.Connected) (hn : 5 ≤ Fintype.card α) (h : ∀ v : α, indepNeighborsCard G v ≤ 1) : 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