Source labels openChecked July 26, 2026

Reed's omega, delta, and chi conjecture

The simplest open case is when $\Delta(G) = 6$ and $\omega(G) = 2$ .

Combinatorics AMS 5

Mathematical statement

The simplest open case is when $\Delta(G) = 6$ and $\omega(G) = 2$ .

Statement source: Papers 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

reed_conjecture_

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem reed_conjecture_Δ_6_ω_2 :  ∀ {V : Type} (G : SimpleGraph V), G.emaxDegree = 6 ∧ G.cliqueNum = 2 → G.chromaticNumber ≤ 5 := 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 B. Reed, ω Δ and χ, J. Graph Theory 27 (1998) 177-212.background openproblemgardenbackground mathoverflow/37923background