Written on the Wall IICombinatorics
Written on the Wall II - Conjecture 19
WOWII Conjecture 19
Mathematical statement
WOWII Conjecture 19
If G is connected then the size b(G) of a largest induced bipartite subgraph
satisfies
b(G) ≥ FLOOR((∑ ecc(v))/(|V|) + sSup (range (l G))), where ecc(v) denotes
eccentricity and l(G) is the independence number of neighbourhoods.
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
conjecture19
theorem conjecture19 (G : SimpleGraph α) [Nontrivial α] (h_conn : G.Connected) : ⌊(∑ v ∈ Finset.univ, ((G.eccent v).toNat : ℝ)) / (Fintype.card α : ℝ) + sSup (Set.range (indepNeighbors G))⌋ ≤ b 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