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Erdős problem 760

The cochromatic number of GG, denoted by ζ(G)\zeta(G), is the minimum number of colours needed to colour the vertices of GG such that each colour class induces either a complete graph or independent set.

No current result

No reviewed Result is current in Vela Mathematics Program. Retained source material is shown below.

Retained declaration

FormalConjectures/ErdosProblems/760.lean

Formal Conjectures

FormalConjectures/ErdosProblems/760.leanErdos760.erdos_7604 linesExact file
True ↔  ∃ c > 0,    ∀ (V : Type u_1) [Finite V] (G : SimpleGraph V) (m : ℕ),      G.chromaticNumber = ↑m → ∃ H k, ↑k ≤ H.coe.cochromaticNumber ∧ c * ↑m / Real.log ↑m ≤ ↑k
SolvedProof has a holelean4external proof

The proof uses `sorry`: part of the argument is written but not proved. Lean accepts the file; it does not accept the theorem.

Proof manifests naming this Problem

  • Jayyhk Erdős Leanjayyhk:erdos:760
  • PLBY Lean proofsErdosProblems.Erdos760

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