Written on the Wall IICombinatorics
Written on the Wall II - Conjecture 40
WOWII Conjecture 40
Mathematical statement
WOWII Conjecture 40
For a nontrivial connected graph G the size f(G) of a largest induced forest
satisfies f(G) ≥ ceil((p(G) + b(G) + 1)/2) where p(G) is the path cover
number and b(G) is the largest induced bipartite subgraph size.
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
conjecture40
theorem conjecture40 (h_conn : G.Connected) (h_nontrivial : 1 < Fintype.card α) : ⌈(((pathCoverNumber G : ℝ) + b G + 1) / 2)⌉ ≤ G.largestInducedForestSize := 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