Theorems · Theorem · combinatorics
SimpleGraph.chromaticNumber_top
∀ {V : Type u} [inst : Fintype V], ⊤.chromaticNumber = ↑(Fintype.card V)- Cited by
- 4 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Fintype
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement and proof · cited by 9,680
- Fintypestatement and proof · cited by 7,736
- ENatstatement · cited by 4,985
- SimpleGraphstatement · cited by 3,072
- Fintype.cardstatement · cited by 1,386
- SimpleGraph.chromaticNumberstatement · cited by 54
- SimpleGraph.Coloringproof · cited by 44
- SimpleGraph.Coloring.colorableproof · cited by 12
- Finite.injective_iff_surjectiveproof · cited by 9
- SimpleGraph.selfColoringproof · cited by 4
- SimpleGraph.Hom.injective_of_top_homproof · cited by 2
- SimpleGraph.chromaticNumber_eq_card_iff_forall_surjectiveproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- SimpleGraph.Coloring.surjOn_of_card_le_isCliqueproof · cited by 1
- SimpleGraph.chromaticNumber_top_eq_enat_cardproof · cited by 0
- SimpleGraph.chromaticNumber_eq_card_iffproof · cited by 0
- SimpleGraph.chromaticNumber_le_cardproof · cited by 0