Theorems · Theorem · combinatorics
SimpleGraph.Colorable.chromaticNumber_eq_sInf
∀ {V : Type u} {G : SimpleGraph V} {n : ℕ}, G.Colorable n → G.chromaticNumber = ↑(sInf {n' | G.Colorable n'})- Cited by
- 5 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Set.ofPredstatement and proof · cited by 6,101
- ENatstatement and proof · cited by 4,985
- SimpleGraphstatement and proof · cited by 3,072
- iInfproof · cited by 1,690
- InfSet.sInfstatement · cited by 935
- SimpleGraph.Colorablestatement and proof · cited by 67
- SimpleGraph.chromaticNumberstatement and proof · cited by 54
- ENat.natCast_sInfproof · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- SimpleGraph.Colorable.chromaticNumber_leproof · cited by 11
- SimpleGraph.chromaticNumber_le_iff_colorableproof · cited by 10
- SimpleGraph.colorable_chromaticNumberproof · cited by 3
- SimpleGraph.Colorable.chromaticNumber_posproof · cited by 2
- SimpleGraph.card_le_chromaticNumber_iff_forall_surjectiveproof · cited by 2