Source labels openChecked July 26, 2026

Written on the Wall II - Conjecture 144

Mathematical statement

For a simple connected graph $G$ , $\mathrm{tree}(G) \ge \mathrm{girth}(G) - 1 + \mathrm{ecc}(\mathrm{Centers})$ where $\mathrm{tree}(G)$ is the largest induced tree size, $\mathrm{girth}(G)$ is the length of the shortest cycle ( $0$ if acyclic), $\mathrm{Centers} = G.\mathrm{center}$ is the set of vertices with minimum eccentricity (the center of $G$ ), and $\mathrm{ecc}(\mathrm{Centers})$ is the eccentricity of the center set , the maximum distance from any non-center vertex to the nearest center vertex.

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

conjecture144

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem conjecture144 (G : SimpleGraph α) (h : G.Connected) :    (G.girth : ℝ) - 1 + (ecc G G.center : ℝ) ≤ (largestInducedTreeSize G : ℝ) := 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

Pinned Formal Conjectures sourceformalization Conjecture 144background