Theorems · Definition · combinatorics
SimpleGraph.chromaticNumber
{V : Type u} → SimpleGraph V → ℕ∞The chromatic number of a graph is the minimal number of colors needed to color it.
This is ⊤ (infinity) iff G isn't colorable with finitely many colors.
If G is colorable, then ENat.toNat G.chromaticNumber is the ℕ-valued chromatic number.
- Cited by
- 54 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Set.ofPredproof · cited by 6,101
- ENatstatement · cited by 4,985
- SimpleGraphstatement and proof · cited by 3,072
- iInfproof · cited by 1,690
- SimpleGraph.Colorableproof · cited by 67
Cited by54
Results whose statement or proof uses this declaration.
- SimpleGraph.Colorable.chromaticNumber_lestatement · cited by 11
- SimpleGraph.chromaticNumber_le_iff_colorablestatement and proof · cited by 10
- SimpleGraph.Colorable.chromaticNumber_eq_sInfstatement and proof · cited by 5
- SimpleGraph.chromaticNumber_le_of_forall_impstatement and proof · cited by 4
- SimpleGraph.chromaticNumber_ne_top_iff_existsstatement · cited by 4
- SimpleGraph.chromaticNumber_topstatement · cited by 4
- SimpleGraph.colorable_chromaticNumberstatement · cited by 3
- SimpleGraph.two_le_chromaticNumber_of_adjstatement and proof · cited by 3
- SimpleGraph.Colorable.chromaticNumber_posstatement · cited by 2
- SimpleGraph.Walk.three_le_chromaticNumber_of_odd_loopstatement and proof · cited by 2
- SimpleGraph.card_le_chromaticNumber_iff_forall_surjectivestatement and proof · cited by 2
- SimpleGraph.chromaticNumber_mono_of_homstatement · cited by 2