Source labels openChecked July 26, 2026

Written on the Wall II - Conjecture 291

WOWII Conjecture 291

Combinatorics AMS 5

Mathematical statement

WOWII Conjecture 291

For a simple connected graph $G$ with $n > 2$ , $\gamma_t(G) \le k + \mathrm{frequency}(t_{\min}(v))$ where:

$\gamma_t(G)$ is the total domination number,
$k$ is the first step in which a zero appears in the Havel-Hakimi process,
$\mathrm{frequency}(t_{\min}(v))$ is the number of vertices achieving the minimum triangle count.

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

conjecture291

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem conjecture291 (G : SimpleGraph α) [DecidableRel G.Adj] (h : G.Connected)    (hn : 2 < Fintype.card α) :    G.totalDominationNumber ≤    havelHakimiZeroStep G + freqMinTriangles 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

Pinned Formal Conjectures sourceformalization Conjecture 291background